Network Formation Game

Click to edit Master title style

Click to edit Master text styles

Second level

Third level

Fourth level

Fifth level

‹date/time›

‹footer›

‹#›

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/master03.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADngMAAAUALgAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC3QXRBwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////9wF 0AfcBdAH////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABAAAAC0BAAAEAAAAJwH//xwAAAD7 Aob/AAAAAAAAkAEAAAAAAEAAAEFyaWFsAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAC0B AwAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAhYAAAAyCuMB9QAKAAAAQSBDb250cmFjdFEAIgBY AEQARAAiACkARAA9ACIABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAA AAAYAAAAdGkTAAEAAADkBAAAAAAAAAQAAAAtAQQABAAAAPABAwAcAAAA+wKG/wAAAAAAAJABAAAA AABAAABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAtAQMABAAAAC4BGAAEAAAA AgEBAAUAAAAJAgAAAAIJAAAAMgrjATYDAQAAAC0AKQAEAAAALgEAAAQAAAAtAQQABAAAAPABAwAc AAAA+wKG/wAAAAAAAJABAAAAAABAAABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQA AAAtAQMABAAAAC4BGAAEAAAAAgEBAAUAAAAJAgAAAAIfAAAAMgrjAV8DEAAAAEJhc2VkIE1vZGVs IGZvciBRAEQAPQBEAEQAIwBmAEQARABEABsAIgAiAEQAKQAiAAQAAAAuAQAABAAAAC0BBAAEAAAA 8AEDABwAAAD7Aob/AAAAAAAAkAEAAAAAAEAAAEFyaWFsAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAABAAAAC0BAwAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAi4AAAAyCnUC7gAaAAAARGlyZWN0 ZWQgTmV0d29yayBGb3JtYXRpb25YABsAKQBEAD0AIgBEAEQAIgBYAEQAIwBXAEQAKQA9ACMASwBE ACkAZgBEACIAGwBEAEQABAAAAC4BAAAEAAAALQEEAAQAAADwAQMAHAAAAPsCp/8AAAAAAACQAQAA AAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQAAAAuARgABAAA AAIBAQAFAAAACQIAAAACGAAAADIKswPsAgsAAABTaGllIE1hbm5vciA7ADEAFAAxABkASgAxADEA MgAxAB4ABAAAAC4BAAAEAAAALQEEAAQAAADwAQMAHAAAAPsCzv8AAAAAAACQAQAAAAAAQAAAQXJp YWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQAAAAuARgABAAAAAIBAQAFAAAA CQIAAAACHwAAADIKlAShARAAAABKb2ludCB3b3JrIHdpdGggGQAcAAwAHAANAA4AIwAcABEAGQAO ACMADAAOABwADgAEAAAALgEAAAQAAAAtAQQABAAAAPABAwAcAAAA+wLO/wAAAAAAAJABAAAAAABA AABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAtAQMABAAAAC4BGAAEAAAAAgEB AAUAAAAJAgAAAAIQAAAAMgqUBPcCBgAAAFJhbWVzaCQAHAAoABwAGQAcAAQAAAAuAQAABAAAAC0B BAAEAAAA8AEDABwAAAD7As7/AAAAAAAAkAEAAAAAAEAAAEFyaWFsAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAABAAAAC0BAwAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAhAAAAAyCpQEvgMGAAAA Sm9oYXJpGQAcABwAHAARAAwABAAAAC4BAAAEAAAALQEEAAQAAADwAQMAHAAAAPsCzv8AAAAAAACQ AQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQAAAAuARgA BAAAAAIBAQAFAAAACQIAAAACGQAAADIKlARVBAwAAABhbmQgSm9obiBOLiAcABwAHAAOABkAGwAc ABwADgAkAA4ADgAEAAAALgEAAAQAAAAtAQQABAAAAPABAwAcAAAA+wLO/wAAAAAAAJABAAAAAABA AABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAtAQMABAAAAC4BGAAEAAAAAgEB AAUAAAAJAgAAAAIWAAAAMgqUBHEFCgAAAFRzaXRzaWtsaXMeABkADAAOABgADAAYAAsADAAZAAQA AAAuAQAABAAAAC0BBAAEAAAA8AEDAAMAAAAAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/master02.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

<= /div>

‹h= eader›

<= /div>

‹date/time›

<= /div>

‹f= ooter›

<= /div>

‹#›

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

A Contract-Based Model fo= r = Directed Network Formation

Shie Mannor

Joint work with Ramesh Johari and John N. Tsitsikl= is

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0022.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

The Context

&#= 8226;Nodes/sensors configure themselves

&= #8211;To establish connectivity

–To be able to deliver traffic (after possibly multiple hops) =

&= #8211;Prefer fewer links

&= #8211;Dislike too much traffic through a node

= 226;Centralized management versus = ; selfish/strategic behavior

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0023.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

The 3 Pillars

&#= 8226;Traffic:

–P= rescribed traffic from i to j is = Bij

&= #8211;Traffic must satisfy flow constraints

&= #8211;Shortest path routing

&#= 8226;Bargaining:

&= #8211;Connectivity cannot be forced

&= #8211;Links are formed by contracts

&#= 8226;Directed links

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

The Basic Model

•G= raph G of <= i>n nodes

= 226;Nodes wish to communicate between themselves

&= #8211;Communication is expensive (power)

&#= 8226;Cost increases with amount of data (but not with distance )

&= #8211;Connectivity is imperative

&= #8211;Number of hops is not important(?)

&= #8211;Establishing a link may be costly

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0001_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAB AAEAgAAAAAECAwICRAEAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Relevance

Applications:

<= span style=3D'font-size:88%'>•Storage Area Networks (SANs) and SSPs <= /span>

<= span style=3D'font-size:88%'>•Internet/Peering for non-QoS traffic

<= span style=3D'font-size:88%'>•Privatized Mail (!)

<= span style=3D'font-size:88%;visibility:hidden'>•

•Part of the network formation sub-field includes: = = trade networks, knowledge sharing networks, buyer-seller networks.

<= span style=3D'font-size:88%'>•This work focuses on traffic and connectivity.

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0003.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

The Node’s Dilemma

A wishes to transmit data to 1.

Given the current topology,

A can try to establish a link to

1, 2 or 3.

Short (cheap) links -> more “unsolicited” traffic

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0003_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhagBZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALBMAAABA AEUAgAAAAAAAAAL/hI+py23honyhzmRB3befzXng6InjiaZnea0myrYgm5GxY9+Yjs/8/lv4gg+i AgIxfpRFJiKphDo10l91er1lpktiFhv8gq1chnhyHmvL5nTDrS7BnXMg+y2/R+pNPb7lt9fBx7WF EygBR1jmtsiGZIaIFnIkuTf0ZJlISWXYpUnB4RIK+qFSMwOpqsG66toK+3q6ham5kkNRakpbq/tU hevb9+sJ2ggpnNlT6ujo68ycnKcnxgcdXSgod20rLYLIzRo2eR0uw/m9Nog+TV287Wcufug9L8SO 3faej9Gr+4VPmLxA++r1Q0XDn5cUCQOGmQWRYSGJLwo+tODwjUIjBYac8SkAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0003_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhQgBHAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAA/ AEQAgQAAAAAAAAAA/wECAwLxhI+JweoaDmuv2jXjhTnvn3TiSI7gaXRoSq6guk4A7FZirbF57dB8 +LPJghBij2KUJBfLYhPZVC530dS02ktSsTPjltsNfrnjFzjLg56lrjLYbVvHY/IH3FlHm/P6zX39 NxN49jdI6MeHaGEIaIWXuKjmCGnnAWQgQMkxJNgg8KnZ85mZMQoammAqMKHa6voKGytr2mGKmkpr eXqLaevDezCKwQlcKVkccozct2zXrPhcGT03zVw9ec2Urb3N1q08zcgrjkpe3u39jc6yHrZurgkf 327pHgNO1NJW/6SPclOlhMCBxPoB/PfLYLoXBSsUAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0003_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh2wBZAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADE AEQAgQAAAAAAAAAA/wECAwL/hI+JwaGvnGkS2ouz3vy1fjChCHIU2Z1fybaue5bq+kLzjeP1zvdA DgT6EirZbYhMZoqpo/JHa0Kjz6oyBvpgkVsYygoedk2Lr29cq4TXXmr6SRGz5y/3O+kw79T0vsZe dwXnR7hUxbd3iFjI+HPIZbXY6Cd5Zhk5mVnZs5my1pmJCQa6QZoYSml6F8imisrZevr5Oucqy2Kb lkuLS7cb0vfLSxbcIgwzLOqLe4ycjEe42+z8fDZtnNV4XT3BaLuNzX0bTewNnnzeW6opzjpJmh7e rv6+FC8/X16PcW+sl2+jHzNJArPEAWgoFJpuqA4itFDQiBlA3gRYFPCQCMVC/wEujtjo56LHjFP+ NRKJkQkqlBhJqgzFsoEAk4VYkpwyMyIImwxGrkR5U2bLV0AniPx59CaUpEgT2Dw5VKlTppMsQvDJ KKrUqVZXWsAaUutWBFSrYugaduxXA2JramgbBq3aC3D71HVKR+5cupnu4mWjdy/fkx389ggseG3W nXETM3b7WAlix3QNS7Y89TLlEpiRdP47ZPLms3Y/g+ZhevSB1DVYrz7sWjWA2Jxpz94hWnaG3KFx t7YtG/hb4bGFBzc+GHdq3ro5IFeMeudz3dNPR9/AvHlhK9MtZ9ce2bPks9XBf8eOsXxbq+fBh1cO 9rCC+O59tN9NXznZ/PWvw00uz1ZXRZlAU3+rycUaf6jFJFGB/QGl4FVl2XfRQvxYaCBLEc43oGcV BgEiSO5pSGKJJD4Rk4MeOGQghx5t6OJ9hfkkjYoPIsgCjAYUAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Cost Structure

•<= /span>Every node suffers a cost:

•

•<= /span>

•

•<= /span>Terminating traffic is counted, but not originating traffic

•<= /span>For simplicity all links cost the same (0)

•<= /span>It is good to be a leaf

•<= /span>Routing is part of the topology, we assume shortes= t path routing

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0006_image005.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC51Uz2vTYBh+v69p2qR1zeqUUaXEHWRjOGEH8SIUPVQPDnXFc7OR0YVmHUuhBjzs MHaYHkT0MgQ9jQr+CR56EkE861VheNEhDE+i8Xu/X9qSgRpI8j5PnvfH8/Hle/f21S7wq1aFHFgY 3awTDDLPKQCF0/xrlt0WVRElREaEJknCozkyKbmC1hUp5GrVMovOmiWoQIJicBgesGgPURVgz2Q5 UlOE61631YjXfYAbBHt/p5s/xYQPsCkYFJzGauhH7oLfc291Qm8N3j897H1gt+t+672ZXIkNpjvH 1EX2nrefmbslNLbhe8stb6ntQ17ytRKWdLVus2Aj1pfiB7l0Hox0vgZpfNO4WEnn75xM5z+PI7/W 6Uo+L/mH42JuhZ84uOSrkcILDv+usfQZqbrpPptGus+mke6T1R3xKfr1yYsT2G8mUjg/gXg6siT2 SxmRB0pxcIxP6CpFv2DIykpxocBrauzYiOsa37d4D40Ps6Li6B4i/7SHCOD7K0tSa/mRr2Wg+2xP DM9xu4z4ssZXxxB72tljEyuutDs97d1AxXJbKdYJrs50fUYr5gAVV+rCi5v8nxeQXoj0co02jvN9 Ewicpyb39hufsobxo+wwPk8EFnMNfvzxn1KcazEOlzptgIOK/aW1X/7LNSb0Lt+/+0HK/z9UNxyz 7x1dd9Rvn0zxXTYbKPw6g/hSYMvTx+YnFD9mQPR22KGI10t+phFKpxbjqOuHEGMfYBlnYIcn4GPr UxlGPWV4/i8O/729aAUAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0006_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgFMAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABwDb AEEAhAAAAAAAAAsIBQUICwsFAAAABQgIDQ0IBQUIDQ0ICAAFCw0LCwgFCAsLDQUFCwUAAAUABQAF CAgFAAAFBQUFCAgFBQsFBQgIBQUFBQsLCwsICwsICAsIDQgICwgICAECAwX/ICCOZGmeaKqubOu+ cJwKQW3f9yDvKVEXhgOilNCJfDXFgtFYOHiwxcNm5C0gDRGthhACrlmo+HSoRcIlaRWATLLApLaS gTWVFaKFBEg6nAFlf4ABRgIGYytXQRMQhzwHBVl6kUcBQwAJjYibImUBlCZFJQKRUngpkGiBYWUD mY6dliQLFKqnZZcjApeinCcERn5oMXAApLCAVZnDLgsVzJsJU3xpT3F4eoImxYO5WkPLItKnI04j 4eMmhuK1viWpR2sxwHkP5CgC983P7uXTyCekDNGjL44ye+oc5dNCLaAEIwRAoQjXTAIXFXp+NKng KCOhjIIsGCD4RVO3FRRf/ziDpuXTBW0qLcpCRSkiy5KwbKpYlu0mID4988j8lAUeGxxuxD0YIkDe r1MJ2knToehnUaBPjNLIJS3pl6XE+KWRgO2B04o1zra8SDNM0C9DKQk0pYLAH7p9COmCmUKgSrDG sD0UCq7RAgya1pFipbcc2VlmXbS5QY7AKT3eZFjuO3jqDFB4R7TyNyD0tsFf9S0esbmFsBfhMFvN o0mRhQxLe63G9EAbSdJhmRlNKYOWz1dHJI4CjZDE7q86dJZjskRCroiwfn+9jjTAqYVpmJwQcBeC hgbg2dx9gAGBGgYZmBg9mkv79uAl6MG9LF4lRxXkSSIBX6JJhJ1j9/glDf9oJjmT3QOgSJNLgC5Q SCFnwSiwAQevHSOUYA1VVc9M9hHXwkr5lUUIBzwQkFkakR2lFk7+RAiYOHXAZQModv0Xxw2COBhT WqwRiJwxjSHhm3hC2pWFfroAOUx6/gn3A241ETjDjEje0BAKUFZiA0xUoiDEOi3sgogX6hQkA5si vpFjP328iIqbUYhngSQmyenTCHsu0IFrXL6wp3MKmLjDoTgCFNCNdAL65yztmGlnC0diBCkK5gCw waRlWmGNaEQh0mk5cwaUaqRfjJqIjyiIxIJdGVg3y6pp4EpGY6zuWigUo/UqRrAruAigcpZi4qiw zDbr7LNbdOflpAAc+un/s9hmq60vnkgrZSJPJODqtuSWa26zrah57rrstjvGEhmI5e689Nb7y5f2 5qvvvvz26++/AAcs8MAEF2zwwQgnrPDCDDfs8MMQRyzxxBRXbHEUm16scbM6+bXxxwbLBvLIzXpM Msg+BAnWFsqpYdFlMp0hhUYng3yAETMjEFUW144IBCQjDdaThDWPLKtSOjdHBFivDJdbxkVTvPM5 TE+hD9ES7qYG0VFr3BQJXJ9ENThL4VJP0pd2/bDISCfgSJhYLzVJFgGGrfbEKc1cgAdTeAfZJ3x/ ErQZApZ6t8RfH674iY0ouvjjf2sJ+eSUV2755ZhnrvnmnHfu+eeghy760uikl276vCZPtGnqpw+c 805TePN66wbbfYLtttMecO5LZ8a77sJOBWETMhViA8xuTPXyWn4rLzhvAxUPfK+eyPWfhEQDrYcO uCwYBBDZgw/hITZJKOTv0yPCdbdEtvSzclj3SYP4lwgkIfu8pu/O+nzR4Eojrxkb9JD0PwNwbWtl k5z+OLE+5cCjaV+KWxco8QquVbBsyFrg/gATlJsBzRhA+E0RJPjBYxCNJOYbUFF+pcG/sGVmfvMI BmIHwwjgBnDT6IBMZmiJaFHlHzDEEwBCAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Example

Flow thro= ugh 1:

2 to= 1

2 to 1, = 3 to 1

2 to 1, 3 to 1,= 4 to 1

2 to= 4, 2 to 3

2 to 4, = 2 to 3

3 to= 4

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAAAAImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAm AAYAgAAAAAAAAAIchBFxy+2W0onq2Uez3rxnRF0io03SiIIRmaZnAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAl AAYAgAAAAAAAAAIcRA6py+2xjnS0qmkktJzpD4biKHZmgmXb2a1AAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAG ACYAgAAAAAAAAAIlBIKGy73HYDKHKlttwFvz74VUN4KleKHZyabt6sbw2kjko5BpAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAA/wImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAA/wImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAm AAYAgAAAAAAA/wIchBFxy+2W0onq2Uez3rxnRF0io03SiIIRmaZnAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAl AAYAgAAAAAAA/wIcRA6py+2xjnS0qmkktJzpD4biKHZmgmXb2a1AAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAG ACYAgAAAAAAA/wIlBIKGy73HYDKHKlttwFvz74VUN4KleKHZyabt6sbw2kjko5BpAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAm AAYAgAAAAAAA/wIchBFxy+2W0onq2Uez3rxnRF0io03SiIIRmaZnAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAG ACYAgAAAAAAA/wIlBIKGy73HYDKHKlttwFvz74VUN4KleKHZyabt6sbw2kjko5BpAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAl AAYAgAAAAAAA/wIcRA6py+2xjnS0qmkktJzpD4biKHZmgmXb2a1AAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAm AAYAgAAAAAAA/wIchBFxy+2W0onq2Uez3rxnRF0io03SiIIRmaZnAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAA/wImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAl AAYAgAAAAAAA/wIcRA6py+2xjnS0qmkktJzpD4biKHZmgmXb2a1AAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAA/wImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAA/wImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0014_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAG ACcAgAAAAAAA/wImBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyargS7YrhUiQjd82WwAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Centralized Solution

•One can try to solve the optimization problem for the whole network and look for the “best” topology in terms of aggregate cost.

<= span class=3DBB style=3D'position:absolute;left:-4.43%'>•Best solu= tion is a perfect graph

Does not make sense – we want as few

links as possible

Add fixed cost per link – problem

becomes hard (NOT MST!)

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0005_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAG ACMAgAAAAAAAAAIjBGKJGnttmnwzJnsdVvd07WXfKJacuaXhyaqgI8VxVFW0WQAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0005_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAf AAUAgAAAAAAAAAIXhBFxy43KUnJ0SXiz3hzLCl7NBFKkUQAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0005_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAG ACMAgAAAAAAAAAIjBGIZaMvnYHTxpHbtfXhnrinf6JWi2Z1qyobtQ8VLU1W0WQAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0005_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIgAlAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAe ACIAgAAAAAAAAAJohBFxy42dkpsrmoiz3hlhCnaXBE4WVJrpyrbs2ZLOV4ozTdkQHMr3U+OFapeX QuUazZIVFLN58D2B0unjaK1gs9Hq9Li1ysJMKdl1Pq/UXmJOzZDAo8V3O3735EdCbd//pzeHx/a1 UAAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Social Approach

•Every node is altruistic, allowing each = node to connect to it •Impossible to guarantee minimality of network – will end up with the perfect graph and many redundanci= es = 226;Specific nodes may suffer a lot of traffic without being compensated

<= span style=3D'visibility:hidden'>•

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Negotiation Process

•Two nodes form a contract:

–Node i pays node = j

–Node j receives traffic from node i and guarantees it reaches its destination if possible

•i compensates j for the excessive traffic sent through j

•j can decline to the contract, but for a high enough payment j should ac= cept

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0024.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Negotiation Process

<= span style=3D'font-size:88%;color:#CC0000'>• i offers $pij to j, to form link ij

<= span style=3D'font-size:88%;color:#CC0000'>• j demands $qij from i, to allow the link

<= span style=3D'font-size:88%;visibility:hidden'>•

<= span style=3D'font-size:88%'>•A link is formed if pij ≥ qij <= /span>and pij > 0;

• payment is pij

•

<= span style=3D'font-size:88%'>•A strategy <= i>s is a vector of offers & demands

<= span style=3D'font-size:88%'>•Given s, a graph G=3DG(s) is defined.

<= span style=3D'font-size:88%;visibility:hidden'>•

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Payoff

<= span style=3D'font-size:88%'>•Given that graph G was generated by= s

<= span style=3D'font-size:88%;visibility:hidden'>•

The (static) game is now fully specified

Note: it is not clear now if it is good to be a le= af

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0025_image029.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC5WTv0vDQBTH3921to3V1LiIOEQFsYNFnHRQBEEnFdr+A4oRI9YWUqgZhCJOxcFJ 8Afo7CA4Cg5OTuqqo0KLTlIQBxGN9y65YEuFenDkfXLfd9+7l7z72+sDEEPXigwiGJ3PEwwYpQAU esRqkM8IlRElxIsIdRxHRAnS5b1r9XVRWmS6pvFooEWFbnBQDDHOVzw64/Oxg2cynuNpojC7kF9J 2zkDoCq8P2nx2z3hLppCgEIsbWYMS58zCnoym1lYh4fjt8ITn7r+XtjXlssBrhvi6jB/jignJN2B qXFbciKGPOPzqYo8aLt+uiP9yL/8COCz6vsCHRP7mp6PyjaV374qy4uSmqtSPxn9zSo7DAq9z3sB XF81pX4jVMv94sSmWV838s+6ufcgfv1G23GHKVPyVityzudSi8sRj5cIw3pacUMqpgEVSavBF6V4 spSdWcyuAVx0Kt83Fa3JCp+Q4TbcYsiSvBSu5QmGPO75Xn395XsUUib/9q2vyAfZjuAWFUvyTsDl +j+owf2c5u+nslfhc2dJjgZdVrx+UURPicbwuiUGIUGXogsJpX0p28obGSijD/CMXii5CXy8PGtQ f0cmVn4AT/Z54hoEAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0025_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhQQFDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUACQA3 ATYAhAAAAAAAAAsIBQAFCw0LCwUAAAAABQgIDQsFAAgFBQsLDQ0IBQUIDQ0ICAUICwUABQgFCAgF AAAFCAUFCAUFCwgICwUFBQsFBQgIBQsICAECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquqhC8 cCzP8cDeeH66dO/buqBwSCwaj8gcoeBryoDJKGrprAag0qx2y+0GqS/DIYd4Yb1JcEBMNqPf8HiK kFCoFoxugxke4/ZnckR7MGx/BYGCiiQLiTcIeSqENA45DQ9+cxB2XJNrmSwIjouWfJ9ko6Q5CzKV BJsqBBESnCRqL3kNmbK0K2UBkVQGtSkNE8QpAqBansM4japGzcgp0NFDZYYAsm5ziCbcvSKTkSK8 1CR7zuZMqQCX6CcNFGishfElBPTXRPZh+Lb28XuG60SZcuBmIaNSKV8EYPkKiDvBaiKAbPguLYv1 ACASfwEsDtwCUuRIIy60/5XQmEzltnZTCiAUwaqhwQA2RWTbyM6dw5kkY5g8GaWkR6Is7AEdQeAY ij0iMSbLaS6Cy6oQmT5c55DrDVlUufB4MRTpkbEhj5o9QSWVvhRlqBJyW2HHFXkFvM5F4SLsL1oC EMrymQQt4TtpuaU9afhIRQWKy27ZSWSJSx5LWaij5mIiN69M84LilisvsXNxGmODMYBlGcmKVAv5 dcX14jd7+605vZUnCypA446wB3qEizNQOS2wuMQiWh+ZfdWo/NCCOHW+SdG+O4SbdU7Y4WAu8vo0 k+JfH5659c9b1hGbxwkcJ1FtlO1hvzKZGJ4o/u771dKfF59ltwI3yJ1HDf9I3ZBQXjqmvSMaYqCF Ew8rh0lBW36aMYHQgCdtOAQhH06IhjD2gQOTLef5RshVF+1GQmd2cMOhCMdR1GAJOSpiIxE0MiKj EM/1EN0cD924QpDDDYlDkTQIFmBlK4Z2ClsPDSXVCMLheNtNHPIQFmmLYEjeezpxh5SZRBxUQhkZ FkEFbLFUyeULHFp4E1fAwWdiQjCmCRqIcCRHpVd9ImUogIh6CMdnKUakZpNf2pIlOlsCwAqfScaE Hjs48VgpAFDOcKQ3n97w2IyTjmRZpCWsalyrXqRkYCzqJVSQrlp+yaSXninUHDEL5NSXpWi+IUug T4Ya2qcIOIPaiVbduqT/s+xwKk60sBZjpwkX+DFtjCYRYpKeDqnJ0EqOqniGKKyWSGcWXVL33rLW KlJvdw+Vg29seGJ55Kbo2CMSuiy+98t6vSWExY8SWuSmHGzKuaJl+QpSMZXcYUwKccREe6vHbPHh 70O0SujMdrt6GQYGQ8LLFD1jyfWNHIsWwSC2N/WSUrc65KxbKyb8TC7QLBQ5k9EO8qyiqcmkrCoU AsR50bxRvIrEsTlUPZzVX0R4ltMUUQ12FtZAiHV6zPpSjjEpLpCqFv8eUXd65UBCYLVI3A1XMBGc +obeRSdbxB5KcgTKBfYR0JEgEyuRwDLx4eC4uJh4Ebnlk7M79zaZg54x/xeXY/l5emubsByxgoOO 9BAb//E4q3GuTlPqQcR+Azyi+mS7prhr8XtCwZvAbRECUPWKR46/LoTQTzLHROJvUk39IPURKT3Z RdskczTJ41p8VeObM7kyMxrIuxxa564uyjBcv0Qw549uudg6VKxY/HPUP/81dDgA+qpxtou0rk7c Q4rf9BMwx6xjXVlY4G/4cL2ShUpuzrPb9NbCwUdYwQkHbEH52vBB6BRmhB1MIRx2VsJC2E9gb2Bh C69kBFmEUIU4pNgMe3C6KWBCAChMyg5p0EMfCjCIOUyiEhlYwCVaqYlOjKIUp0jFKlrxiljMoha3 yMUuevGLYAyjGMdIxv8ymtF40lJIKGBAiwxkkFrbOh1t2vjGM9pRCLIChBfzeLM7+lE8TgtMF7lm nBv+8Y8PMtr+7qLHlbwQYCtbzCJt0Mh0PPKQd/QaTSgZOge1LYVp8xpL3vRJTJpyCoHjUh4Yp6KJ +KOIqiCcDQHAyoi48h6nzCU4Qne5RZphCQyD4qN4iQlfXgGYDhGmLr/4u9XRgRrDYpEhyyQOZ9ah leaZ5jLH+L3wXSQ/ImMELFXhzYsAAQHgVAkGt7nN/22jfnsACsmuVscuBFAZ7oynirSBACSyU4vr fImzbgEFlmlTEOsKqEBZc6cYHPSfXgRiPZcoUYhaFG93nOVFN7rLI04SFIeXqyhHRwoqZTqxLSSF QwgAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Routing Assumption

&#= 8226;Monotonicity:

• <= /div>

&#= 8226;Satisfied by:

&= #8211;Shortest path with equal splits

&= #8211;Shortest path with pre-defined splits

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0026_image031.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBQkGxgZ+AEsTY6MIIYzKWMDAxMDDJgWVYg5mSCsZgYGaEsRqb///+D WXqMElAxbrg6HqYGdgVJISBLjY2fQYrhP0gxgwCQfwDIWgbED4Ca1NiBeqBqeBh8E0syQioLUhkY JjCC7P7N1PAX4sIJYFtZmBgEQjJzU4sV/FLLFYLycxPzGFSYGOt1gVjhAnM9A4MBAwtQnS5QMcg7 RlxibB2izECWhrtmKkwkUACkJi0nvxwmYssNUpOZpVnOARV5ysoE1gVTsY4BVY8L0wwRqLlwkZv8 6GqOcqGa68KUi2KuCxPCXIh/Gf6R519GMP0BqAli0za2dyIgE7JyYHxvVmT+EyY2sHwmnH+bBcJH D3dQlAOhQHBlblJ+DkO9A1DgmgJXDa5wh7iDkQEekrwgIzbnwPj/OUD8EznwEEGRd2Fqh8pzQVMF FzjlMIJdA3GbAAM7mLcHnNYYmZiUgiuLS1JzQTwuBkWGLrBiEOHyRYhB7R9DPXoYMYP1AwAroBNk AAMAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0026_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCAFWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABwAF AUsAhAAAAAAAAAUAAA0LCwAFCw0IBQAFCAsLDQgFBQUIDQsIBQgFAA0ICAUABQgIDQsFAAgFCAAA BQUFBQUFCAUICwUFCwsFBQgIBQsICAECAwECAwECAwECAwECAwECAwECAwX/ICCOJDkIQUAUgXGU cCzP8oC8dK7vfJHwQN0ptWrhgsjaLQnwMWGKwG+RUj2vIkbDEXtUiYAB5IhlisllXXRaJaSZWi7M +3WfRXcs6wd4RCRSb0gME2hDEUcDVFaCJlQUJCwRcgAKlI0yeyJ+gHyYOoSGKIgjimAjllgMAm6l C6SfOVpoUZNdgbGmkCOSlAwVsTGrrXivaMElsyW1lyNengC/WM8kqy7IMnElXrAwA1vYO9/Hq91l 1CPWx+HaJNzrYeClDfCgAuYsu+EmrMsBtjXG7MuhCFqpUc2SlCOTbyA/YiKYzchTzCCPIfo24XKo yNyqABm9AXM4cUFIfv8S/15EERIdR2PVWNIYMNLVyRwsvuA6Yc5ZlWs+QyrgY8pilIymehIUYHFG AaWVjPBi5ApiDFMbd+T8QvTeOjpSgy4jSsUoSEf/6tVYYJXHwphAp17j+QIsxFVkqeK5dynnzZlM gTwlMyTFrigpDCqKS4NO0xlv0wlg3EQq3T5tYua1yrOv4SSL1WYKG/EsiSgQWRB75xPaA6F6MQME cuJxjMHe+LqbvZdy489aSUeFnZoqa42uiW9LCXqy6FtIX3lmrC6LVxF+SVi4NARa0mOIv8CqLVhp 5DDX4T6PlHiHl+i8WVB3bh1W9hHbUXqnojR8lW7VBVEUP910lkx6Btpwgf9pYdSEXVoo+WYdcwfZ BgNu/hTXlmpAIGYhWt6lhx5v0SCom4IM0lSCJIShIGGJFE7Vlj346IXahWF1V0kRxKRyWmwfvYhR CYr8FYMClA2ICoNLzjhHe0CcVxlEN66YIwo/KMAjKs1UKZlwKJ3kpWDCvedKVhoRU9Q4HEYDTHVm RghPOQk94GQXbV3mDIlKrhUjmYzFGUZZT6pZFpuMSAMnk+iBKRmfhCLhBUQd+SLiXhsV9VqJdiyh TqVE8gcPixdCBUM77MWl56MqDfpnEJM6MpuUjXqiKSTDhOGpc6CiZSqpMZEoRKT1HUFrFIEGIEEh JbowVG79QVnoVWy5N6P/oJxC4egh6/kJzXnHlqkss+o8S+SlpaHpU1vIdvsoQ1Zg8EKAExrEjRwn GKDlVfSdGxumj51g5CZK9fpgSH1WQ08ZUnIob7NkfGQvhfnum5tvQ8yoI4hJyEfGeyoOWuAj02J6 TU5z9XObtFMJK5mTHa2zEAO7uGTdi2947A5IIcd85kmxmvwCyi+c4GROFvVyIM4zYFuUBcbSt/Ey I8+mSCtXQ4aCVe3mEPS6M6AWisho2ByL02VBLVnK6lZSNSVZD3rnR1yDabY40qGFZmGMnrbft4Ft cueDOrksA1inhJ0CUPlGrLIwKOgkuYUGu7p35H2j8rdmzgxeWeEJ5arQ/+MkRTSbxaUz0ZA7TKch eupuU4L6Oa2P9iEyD8Q1NuxIKBCfqY1ownvuxjJbBoZIxA270SWozTttC6i6cDjKp868du7WMD0P vnOBfOrC83I77w2hOg4y3TcBfDjhYzf+RNvjjchTrQ6UvgkCPR/2JOThET8mMaOf/u5XivyB5n87 CFL2APgKDBgvIvXT30cAhEBMKFB/HXEgGXw0iArqL3lUqN0HR0hCtIiwhChMoQpXyMIWuvCFMIyh DGdIwxra8IY4zKEOd8jDHvrwh0AMohCHSMQiGvGISEyiEpfIxCY68YlQjKIUp0jFKlrxiljMoha3 yMUuarEwRTgh9ZYwQ/8nWC9yYVxgLsiIBDNyLxCL+BfvULWzOoTBgMvD4z7WAIA4em4gdPSJHfNA EZzgghNtS93uDgKhYiSOgUxSGgRJIjxEvg8Zi8TUyB7JQRq8jmwjVMaPXHa3N+iCPbNyEDY+6TMJ /k8iT/qWKg+XFXrNUR4+MdU3IjiQ8wVLjU2rZb9u2YzjeAOX8RBNwzJHkustyXB3BGYjCpKbV8Hh UqvjnTNLA81CUnMiMtnZJT/RygkNLGQfLFINEHKFIYnzeeWE0TlVqc6V6aQrUAFLsoSSlw8dxVfZ 659WoNK1B3GmWiVhWXDuuZd8/uRjjDJXwrQVnUZCb3BSsmVlUkYKu3D/zlWDM9BUmAnOS36Pb4ep gmKi9xzHDOJSGtXZZTwqmc2AMz7AERBLnSKcf/5IQ7k8gs02pTir3Ct5gRvoMURKsGY0jgd0GJiV GOPTJrFnNRYdqpHGJBte8gtnaMPpfIASmfuIID/rzMp3tFU4HAhUB98r1kF6olEaIA2qTKqcztaG g7LmFABoreZ+LLqktvLVWwRKhG5+2VAuoEgf6FyZOYbwoglyJ6lwjRZQrfTHdF0yYatiqlxH5FgE LAiys2xZixw1IRK1CXI1otK/9qojLb22k9qyygX5xah67gBJhiDWcHKrA5cGYZmy3dCVAmFbquD2 pwdibaPEJMcH7fNM/xb52pro0SZpJFYjCHPRnBbrjs4KDlofg1QiXQVNu4oLssJNE3YR1QrvzrUu vRVvNsjrSNt8TWSW6snUbpUtG4iCFJVj76gIi531pQOZ1lUsXfl7pvZ6TS8Go9WAy7KpXBn4XIhI 8FoliwY6IfZdKP5RspY1L+eY66bgUSjYvIFQr12LSZ8sTZJGIc3+Mna0S1oxuVxMOXRFJZH/1fF4 YwuAh9lSYssBSMX++FR/aQxL65SqH5aat6kgLL7R8OBxsRmvFs8HTUdFj748V2WUXHlvYJYLRCnQ M5g4EmhUoSwtFudW0rFHXZKEHMzsfCBE0Aw5S+sxXN9b503iWU36/f+RZfw80qS9qq5iwa7zIFar I72NX/Cd29b80bokJ/mnY4snZsaZBLRJYdPVmdppPp2bXVQvunWjTCmLwRusKAZzW93ckbJiJ0OC DgiIq25hGTfMbEFOcpMjSJcdebkqBNsRj+Hjed177ANhlNKw2/JpzDvCbG5CjNckN+66MbtpMK19 2txpOh74QgKqT9HBYTU55R0Nej8hrqFSdzBWcZJNuzA088D3sAQeC4I3D9++pJr3HDwQeDdB3xU/ i/nEXIb0ARx28HajGSoYQAs7RNxE0mMJuyfQiO97fiYfCMoLKE2XRxfdyEA4FLwKuwkai+Oui/QI dX4anp8K6Ct0uBcrYaj0KQpw6S98+hSBC/V643yIb626CrPeROIVW+sq9DrDg2hcsKew7KkLAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Equilibrium

•A= set of bids and resulting graph is an equilibrium if:

–N= o node wishes to break an established link

Offer:

Demand:

–N= o pair of nodes w/o a link can reduce their total cost by forming a link

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image033.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjB4oLaAmYETxAqsZgQxmNczMTAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgWMD9QEwKy1Nj4GaQY/oMUMwgA+QeArFVAvECNgcGLGagHqoaHwTexJCOksiCV gWED2O7fTAx/akDWMUwAkUxAKBBcmZuUn8NQ7wAUOCfPFaLCxFivC8QKF5jrGRgMGFiA4rpA1RxA 2ojLlimZFaRVo5IY83oUuN5gN48RTH9AMtebF2SEJtTcR3+q8bszFJc7IeYyQs21YvqvjOxe/OYC 3fuWOPcCzVVFdm/DX0jMTwDHJgvQ3JDM3NRiBb/UcoWg/NzEPAbi3OvAdEcFZEJxJYy/XRHED4Lz 8+Ug9sL4npIgfjCcnyYCSjIaxTB+thBYP5zfzgXiF8L58WwgfgGc78AAtr8YGr//yPMXeng9YFIA x0NmMYx/WAbkzswsGH+zFEjeFc7fKIYqf0WYEYW/hxtVfgo7Kn8nI4SPHj840lM4sfGzXh5kxOIs GL+cGcS3zUIPLwYKw0tZBmREDDb3U5S+oiVARujA3e8uBuKrZ3FB+Qv52IAsBTCAqTHmA6mxgvMX c4LNgPP5wXx1ON+fEcLngpZEXODSCux0aDkkwMAO5u0Bl2+MTExKwZXFJam5IB4XgyJDF1gxiPjw XIhB7R9DPXo4MYP1AwAAaSdgdAUAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhbgElAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQBs ASEAhAAAAAAAAAUICwsIBQAFCw0ICAUABQgIDQ0IBQAABQsLDQ0LCwUAAAgFAAAFCAgFCAsFAAUI DQUFCAsFBQgFBQgICwUFBQsICAUICAUFCwsLCwECAwECAwECAwECAwECAwX/ICCOZGmeaIpCguq+ cPwOhGzfeK7vfO//wGCsYDgIjzJEwohsOp/Q6G3ATCFa0t0gochGFwysd0wum1UsGO0MWzQcXXbQ DZfb73hfOjYQ50cFDDV/PRBchDgIg4hNCw9xeAh1MQtFQwyTUAgBfkCBmVkDARFsgQGnqIdqiySf kJ4MqDWOr08IpEKmqKeqKG64MgOgVgFLUqKdP5vGY8hybsVdm6MzySLLVT8QnCOiAaxQCxK1PtCH 08AmStkwgekpgb1P2+8/8eSa33aii6LDJWtQ3AuyCZwzLxPY/eDXLcA/AHTwqYj4AsxDIdDqlcMk 0cmmi1nojVjWUUlHix1x/2zrVEnhkz4qrY0QeS3aiUDgYhhyWcJNTiRumGFs8DMfyC8MepEUyEDj CJ9CtoFbQCHlEUlWnzaglgKMUpsmDk7h6mJPuKQ8C8l8MhAMWSmuZjrERxHN2hzoSCyoQMbki3hp AXGU+5DmjYIlpnG5BWCAU4xoUSD2JtSFYxuKFey80TbWYyRiTTkV9S7zrctztnJjsyXlx6wiQns+ kfGE6dJzBc+KrMPbrt+rRXhVOI1TgxZLIVNbYGGwjYFmgjLJSzvpK5wQeR+BFrzMFp4MZUiv+Vav dt3ZKwOIG5srEdhAhq9IYIHJ+DnaxcqAXkaXLBWIkUCaCO85wV1RURhSC/80dzH1G4LpKTTgegbU wt9rEI0zhnwmAKaVejzUNhOIf1l3BmIYpmBYTXWIA18O3DUIlImtxEIigPqk6Mt5LHbhYgn8AbDN UQY2QKJ+Xr04Q27COfeck2SIxGF18ogwpJI7mBOYXlX1wF5Yp8goFylTUunSlUzJAw2ERZZnZWUB /uBWOvolwSQZHK4ED5TCbcWmDhcsGIsf3AEXAQSfqdGdbaf8meeiPfHYpz438TnnnpMkKSBwwHWy YpOZiMiepjHo6CGBzpFKQpx9ManjehxhV52bqGZKY1calqBnYsG1pEiltlZ5nwumgJTiq3GJaMKl 6uSGGgCselEntN1F20P/eBBtRSQK04bUq6So0gmMtV5W2NNW9XxHQqCVYFnjtloVc+a3N1r51rPk BmgWGH8isUkym9XqLo6LQIBBGL3RilRlu3bYFAn7CnJEnV/2+VBCWihcVjJlNsyoHxH/NKCIAUd6 CimmVAmjxOZxlaJb1KTc0Ta9DITohDCjbCM+CjapcRCiwHlydkMTUQXJIOYMK1hy9bINpbCCGAgW BWQD01OxxLxzpP0GI++qQyuN6iJIn2nMAhkIyUtKrc3UtQt1kZeKhE5D+HQmxUUQ1CttW/lTXaJB 4dsptvJiRNtUHZ320yp3U7cJd/uYttqoyDSyuYDk6jgkEOTUd7Oc7uLH/+BMwmzM53WhTXnjcYvH cnZiqiFPydWRjTDcmgP5ena2WwNG7GfwO1OiO/buS+6UqNZoTxRkI3yTLD0c3e7Q1ssU8YyOa/2T wKia/UjbQ4vghDVp79I6jIA9LvDqg8/TrzhMfQ3A6Wxivq7YN2H/uew3Bi/kTvsfDDqHHjQE0CoF oo2RXtEzKz0kIOl7EyRooZID3gRzU2BG1dTBigYKCRTPMoMHwfeiX6zMeEFI4Ke4hrW7tA4gUONd CxWYv+BRjwo3eB7slvWGge1tIpjT4e8E1D/IFOVqaihi+dx3BEQVh2m8uh+MlAeW/V2DRPCLILXe oTrMkAV9uaAeADA2vL0lXrEKZjmRxhDVjsnlAAIO0ICG4DgwIMIHjnLsAh2RgMc5/iNxWnRgHnnQ Rz0KUCdv0WFssFDID9axCY08ARmtcEi9bOUQ8vNXv8zRhUwOxSaehFgNg3fJR2YLlLcDwhMNBaRx cBJWSmxT41gTPh1sMINbWgiIGBNIwdXSO7/sZTiIggiofIGYwsQTMou5zGR6Bw6f2wc0Z7mQaZrS mXywJiGEoYBoYlNay/uDN96WsBh+0wnjZEQ6z+mDEAAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image035.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBYoL6AmYETxBKsYgQxmNczMTAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgWMC9QFwKy1Nj4GaQY/oMUMwgA+QeArFVAnKDOwODFDNQDVcPD4JtYkhFSWZDK wLABbPdvJoY/NSDrGCaASCYgFAiuzE3Kz2GodwAKOCtx6agwMdbrArHCBeZ6BgYDBhaguC5QNQeQ NuKyZUpmBWnVqCTGvAkKXGexm8cIpj8gmSvECzJCE+rOR3+q8btTF5c7IeYyQs21YtqmAnYvUeYC 3XuOOPcCzVVDdm/DX0jMTwDHJgvQ3JDM3NRiBb/UcoWg/NzEPAbi3OvANFkVZEIxnP9NEcQPgvPX yUHshfE7JEH8YDh/qQgoyWgUw/hGQmD9cP5LThC/EM6PZwPxC+B8Bwaw/cXQ+P1Hnr/Qw+sB03ll kAlZxTA+kyzInZlZMP4nKZC8K5z/QQxVnlsErB/Ol+NGlZ/CjsrfyQjho8cPjvSkT2z8vJMHGbE4 C8YvZwbxbbPQw4uBwvBKkgEZEYPN/RSlr1kSICN04O5vEwPx1bO4oPwMPjYgSwEMYGp+gfOmFZw/ kwesB85nBacpHTjfnxEizwUtibjApRXY6dD8IsDADubtAZdvjExMSsGVxSWpuSAeF4MiQxdYMYgI eSHEoPaPoR49nJjB+gFp1x0tdAUAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhfAEnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQB5 ASIAhAAAAAAAAAAFCwUICw0LCwUAAAUIDQsIBQAABQsLDQ0IBQgIDQ0ICAgFAAAFCAUABQsFAAgF CAUFCwgFBQgICwsLCwgICAUFCAsICAUICAsFBQ0LCAECAwECAwECAwECAwX/ICCOZGmeaJpCguq+ cOxCg2zfeK7vfO//wKCQUDAIj7EDIoFsOp/QaFNRUx2MUp4CschCGUWveEwu/w6tFwRrhkGW7SAx Ha/b71IF3UVosPEkRA5MgDp9cIWJiot8D10xDA+EimB7jDFvj5ebnHgsN5+LBwFVnS+jf6aNk6pa qYBgry5bmi5giFAQpK0jt6yjlmN9AcTFAYM4W6wivkgKxi0EEctO0tQ9w8bEyDBK1ypEpbMBXFK6 spzP5SPPwWSjAVij60nuAOq1P7ql8PZT6D3gySOX74Sgbyn6cLNVAFe1BvF4MWvI6tlCM81E6Lqo gkaKjEDalRglLgoBCTjW/zDEtRHhRH8d6YErwBEJkYgSD5JQ5zJPgD3zemqsOUJnkH0lCDgSQ2BC QRTDHJ4QOSKoC5I5sL7oAxPITYCXuJbgWQdpVXJClTwt2qBryp9JJwgV4pEhXDe7zko1cS7rXTUl m3yVqLEkWQCDvRChN8zts8B8IfOAJ44ABTKhUDzLC2OxpsZ8IIJNYbEisSUMHl2RktgEVngyA56u 0GAvitU70Yq4KXnKsUnz1halOPZ0gtS45UDkXEbhNYE3SusVvrsAzuJoUxfHJXLx3Nvawl+vPl7j aQoFahzmMZiABZrfp+puoxWArtgn6ovoTlyw9b9kGDXCffGRUN991JH3Cv9/Uq2HCjMXFOhDa4FY h8gwo23VkCb6JTNfc8sZkyFiG46EEwMRPpGNW3El+AIYF91UXmchFjMiiTM+CACKy6wn3UkJwbdb A0TJgKF8uBxJIjfOgSMaCZlUxySRLkmHEXFmQUWllez8hhhKJhjV5A0rJlWjNgYcEJiYVMpnD2U2 NJOlQW1SuJ+XQG43CWh8CIlYmzz0xRdznklJyJjgLSSmn4i6GQcwdxb55yBzDglgmIwCSuZyCwKY CY9JZUpUpdixCACk93ipJTJ2/nlpbg7xWQaph5gmqYbjobqDrgE+SSJ+Ydb2lKxDTFMCGMyJoONu ETblYpDAHmvdrUoWSuP/jK7aw6WCsoknoglUkVBJIL7qwGWrNyxLBkikBmsbjjfakCe5r75BCAYJ WKZsby9sO9OH0rKUbEcDcwvuXcmFayYxRiB7KyQFBKMfVdk0PK1LvBLoakQO9xSlGbyu18vFAp7K hsKWcnwxDApwpORwaRCQYi8zV7zjyoPGOyA6IQM8kaqnMpfwq0FXUdfNMHkzoKl9xijsyBcprVFX uh6QQcQGstRVrWYMU5l16HwyRwlHj5uf1kmUB9KdWBy9m1NZT5KZuH7+4HWF2Nq3h9mFjexOlIc8 8jGddBChc0ysJLatWNWxgezexKn5GFuFhzHTHugeASeUBGFqRB+VPW0f/7CMk/jK45xzdktBunw7 UimlG37C4GcQUxKCnpM75Tq0DwnHSdm8O9HJ0SYj02bF4BcLO/Qg/wc8uwy+/H7FD0933kBAf5om yDtEy76BSBD8N9Pfg5/zu4HZOjHuNKlUQaDeTDz8lpuArLcMm2hM88lXFJta6RufQdKjAwAORUJB EoegUmBA+9SECkFaSAMh8DBl8IKChNBDAemBQdLw6yMEFIEGqOEsZXHQZQ34oBc6SLfDfQ8HYwqH EA7ApP6s6lAhLIEGhDO5IdVQhXPrhAx3Y6xN/VAFO/QLG/CVnxrEMIcDUmEWhkg2pk3NEDksn92W grQ+lUKL4FvBdagIxv8wcVEVWjzAs0L1xfq5RoruWoa+xNWsLLrRPod7QhkRc8YXScJc9JBaENCg LOxRj0MO6VCouBNI4YWxFYL8kvEQ+ZyCwYBvO2vRC0/lEJUAIpI7eVgmdUDBCjSrLTZxSuYG5ABT 5guV6fpQKU+5tT+2onRVWSMrXYnLoxDKhlUZwCxfWbk8qgiWmmGRmnYQFSaAAY432MB/tqcl3TzT BuvLXzNvxq8S8uKa2IAIHMAZBOSJxx0oEqczoUgJdoLrg8scZPV4wABoZk2XMmhgfvCJB31mb570 AeijBCoMZAKil3YzKGG0ZMUYIBQPDz2oQssyCFDGAYMW3QFGHSmRjSIjcAUV5ShmQvrRKHi0EP1I REpnyL6FWqGlLCWaHVYqCpg+IQQAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image037.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBggQWMDMwAlibPRlBDGYDzIyMDAxyIAlWYGYkwnGYmJkhLIYmf7//w9m 6TFKQMW44ep4mIBmCggBWWps/AxSDP9BihkEgPwDQNYqID7Az8DgxQzUA1XDw+CbWJIRUlmQysCw AWz3byaGPzUg6xgmgEgmIBQIrsxNys9hqHcACtxV4nqrwsRYrwvECheY6xkYDBhYgOK6QNUcQNqI y5YpmRWkVaOSGPNiRLguYjePEUx/QDJ3Ay/ICE2ouQ1/IQEJNpeBBWhuSGZuarGCX2q5QlB+bmIe Ay53QsxlhJrrwMTGDzJCoRLGn8EH4lvB+eZge9Xh/MWcIL4OnM/PiSrvzwjhQ/3/D+ZORpLcie7/ B0x7wFGdmQXjT2FH5e9khPDRw4eRwvBp5wKZUJgF48ezgfgFcL4DA4hfnIUlXrDF92Xi/OvAVM4M MsI2iwuaWrnAKRoc3dC0KsDADubtAecBRiYmpeDK4pLUXBCPi0GRoYsRmtsYQl4IMaj9Y6hH9yMz WBYAl2EM3pgDAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjgAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQCF AB8AhAAAAAAAAAUABQgIDQ0ICAsLDQ0IBQAABQUAAAUICwsFAAAFCwAFCAsIBQ0LCwUIDQgFAAsL CwUFBQgFBQUFAAsICAgICwUFCwsFBQgIBQgFCAECAwECAwECAwECAwECAwX/ICCOZGmeaEo6wqC+ cCyrhFDMeJ4ax63/QJgDkQgaZYrFcclUMHzMqGhYlFpxjd41agg8tuBX9xs2NrzldKlbxQ2fZcXB JX1Dr3YSAaHM7bVgDhBzVn93hQiAIntwbgiNW0OKTHmBj3eSh0IQfZaTS4KdkZwlmToKbZGJmkeo aa4riXSSdCIKAV4EdA1kYIYlZwFPe7i9L7wyQwEHERCQKcixhAC0I1kucrVpv6VETjfZVmdFDhJ8 QNUocjcOE6wxwbjy86mma8UjY1JnvfzosjsCiFIzZZWJW8b0Mekiat2/TyVuperWKFwQeyMq2SJU yWIMQYr29Ok4DQXGE4LQ/xCcMkgbgD3GhgwMsieVv3/PrM26FCTePHoRS4q4RsIhk5svAQIRqa6X 0aLLwAl7h0UlS0gKb2m5lfPYtHIU4GiV2rVETZSD2J07YaBRg5k/2OjhCQAhibY+3qo4E5LISwEV /IrAOxTuvV60HFhQJjBFEpYT/6XqMm/mY2oQIkNtPOLWVKK2RmaGkQVKuo8IyLBwGeRbZ4gZU09p IeSCSWc+hqim/cI1Td48qOYIXrDsIuCwS2B4J3NEDTrEVQjSjMWtcR26FwlG0cC6cLsoFALonvf6 ceExLk8XpwQk66KiqSczGBoyacMzqCzPXkdAhnll6VcAf9ghMM8XAhJo0k8E7+FAzBfPXWGAfHOh EaEUD/7VoDUU/kDeFgoYA495R3yYAgG2XRFiGBWgF5GIKsK4ggYuyvAcYSuhcCOJP+xYYxTK4Jcj NQYKaUSQUYQAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image039.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBI0FvAzMAJYl0sZgQxmK8xMTAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgWMCfoCQFZamz8DFIM/0GKGQSA/ANA1iogVtBjYPBiBuqBquFh8E0syQipLEhl YNgAtvs306M/1SDrGCaASCYgFAiuzE3Kz2GodwAKLJPislZhYqzXBWKFC8z1DAwGDCxAcV2gag4g bcRlxXRPEKRVo5IY8yYJcaViN48RTH9ANlcYZIRmJZHutMHlToi5jHBzq7VJcm8ase6t1kV2b8Nf SMxPAMcmC9DckMzc1GIFv9RyhaD83MQ8BuLc68AUoQMyobgSxt+tAeIHwfnFqhB7YXxfBRA/GM7P kgYlGY1iGP+7BFg/nL9bCGw+nD+NH1XejwdsPpyvwQ42H853ZUI134sBoh8SDgz/yAsH9PB9wDRF C2RCVjGMf1wZZG9mFoy/XREk7wrnb5VFlb8gBdYP5/8XYESRX8SFqn4SB6p5E1hQ5TczQvSjxzeO 9GlHbHxvVgMZsTgLxu/jhfDRw5OBwvBUVwYZEQP3DxMXhI/FPxSl33h5kBE6cP94y4L46lmcUP5s UZCO/CIFBZiKfBFQSCP4VmxgE+B8NRawCQpc0HKNC1z2gR0KLdUEGNjBvD3g0pKRiUkpuLK4JDUX xONiUGToAisGER+eCzGo/WOoRw8lZrB+AG6+BxrCBQAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0008_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhmgEjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgCW AR4AhAAAAAAAAAUFCAsLDQgFCAUABQ0ICAsFAAUICwsIBQAFCwsFBQgIDQgFAA0LCwUIDQUAAAAF CAsICAgFBQAABQ0IBQUFCwsLCwgICwUFBQgICAECAwECAwECAwECAwECAwX/ICCOZGmeaKqubOu+ cIw6wjATtqzvfO//wGCLljM5cMKkcsncOQrFkwHarFqv2OzoGTVNu9qweMxlGWrjtHqtLa/OYLZ8 LjsgXAkFfc/vq+x4ekkLcX49BndyXy5TDIYxhI9BiH6LLY0lDg0BnJ0BDyuaoCcOEBGFMpqdp0eo QRKuL6qenKMpB6cumoJis7S2Qw3AW6axML6sSFWwQb6ew3+5wbwkCQG5pQHUmROOKAYQFMaXELzg 2lgV0DzW2BDoMxCJeOJq7TbZ2ykO3d/h4+TMvdOnRF2SewDyDZEHI0G9EuDmgXuYSZiKUtJ6aMoI ANw6JQYsxAAkhaGIiYUq/3yCofLjlYgjULIQta8YkI1RPL4UCYNkSYn/WLRkubKENVulKHgzSpDE rps2t/S74ibUO5dHiSlFcWDrC3BNr2QVkXRpijwXG4SNgTEKP7NMql68qmJswnBwT3TNqwJsRYoy S1Tw+meexk3DmFEtwJdE4BkNAAc1ErmxP47+OgEDF+HCprVkIxd5jGKwZRE+fahKDJDHk9MdJ+8T HVM2ZMLkOJaidgCe0wYce38y4C2ByxjWivaC4FIlZlLlSPRumhSM8AfEndo+4dCRKkHCI2y6Fmu3 dN+Qg9fKblxI8uNxmadwPs78iOkztwO4nl1rFJWJZPOcXQB0tx9u7nEC2v8SMJmAnwsAkvXOcxJS JIKBe2mHoGDKrXbSO4atEOFd5K1AIIYbApHcgkk0WMKDEAYQ4ITGVGfUVhlqZZZwnVi4BW331cNP azGoVKIWOpEwVE+0+AjRdl3hM4FbeM1mIX13UchVkzUCiZqQUzZhpJYMyqekci/wyImT/vgYZUJh 6vhjPTl6Ed2ZLP5wDplOTbUDgffJqAttdbbZhUrUVRmPhRN5F9VMhKZo5zaIZrFnfX7KAChqgg5K p6Ql+VgpdIT5BcCoEp4y4nkhaidNoTNg8GSnIhhJCycZtNrWl3zBWs2RKZiKaqo52PgirRpaRlpZ WQIkLHoOKrVqoK0S8yr/qFvI6hiII9h66wMJ6BqVr76OgNAbdw4brTfGskrqUmO1W82GHibhAE+/ bmMfWQVogG8q+j3J5oVFyWuEfvVqiEqjCjeLR8EB35hXws38SzA1+ybEWEhORFzbwASPYnBNTlJc YbGVBbrOmxey+ygQFWCmbpIjSHABFTqYmh+aoRHW23GaEJaAy5jtChmy9hkdSsqcwndgEUMTm0TM h6JHswiwyPXVnTuvE/RSP3sKL9FdGM1ZEaP2RmdGB9jC8nl0AlsXz2HPm0N/+wGjtg29UWhgTyGe 3a1ve0vns9s+6lxaABSZJrUZj6rLaS64FNF2kNYxzrfcZ9GNpkN376i3/+b7cV4gtnq1Knit0E4e RZ2Xf9mFzjCSmAjVBUoTND5cCyYNWiZYQ9F15iKbkFonoVErpb8TlDEPtWczD+6Di0zb86fyrFeJ Lo68PcbcBi9IArpf37uSzXNHOqfKWWPYUx0pv7zvOQCvXZ4sRB8+UxxaL+T52QNFcjQTKMYx4ADj 0x0GstG6+whCE9USzgNF4gt6vaMTGMMZah7YgGoNJg7euhWtBliLAuJIXyZxwAIvSBDQtcBWQvNE tYr3DBOaBYIXUiADw4LA0ERQQWSh4HgMmIkLAtEpGtwPB1v1wROE8FaGIaFyhIMbHGonQCs84o1a U4pRwIEtZnrNPiz2Qv+vtEc6SAkjYw7mNCF00UF8ehH+1CDG+BHpLiJb4wzIKCIzQiN2eOQXXN5I Rz1KJ47SmSMm4HTHRTYRBZEYyUPwNr+T6PGR1ZhhExbpGEOGwpOPeOSQYuBIkEUyTZPMSwXMcUkf hYsNmIwJKPcxy7pkJGoN+R2F6nYM5NGyfro81BxV5DdN8k8S5rolbIIXzO218TegcQP5gPmfYSph mtwxZjWG2cOYaNNBSwSJSUiwALCNoptWjAkfr9BNI2RqBkl8RDo78k05+rBF4xxBOdG4wXuqUw7z 7NMytWYVBJzylPkx6AAIKYRCZawCdyiFQhl6KkQqQaII3UI8ubHMOVClFAAZnctEzRQEh54PoncZ qS2ot4aPItEVbyElXXZwDlBw8gdPrGFMalDTjtRyDD2dgfw4isxOdjRYdLlpD3JKQMfwNKk/XYNS MzFUgdIBm3zAalG3qimL4sGrWdDqHsTK1Vs8UwuALKta83fWFqSVDm+Fa1sN0QiWsqGuYF2rJPB6 Rykwxq5S/Wteq8BXvR6sgXQciGEXW0TEAsyxZFAsHxTChBAAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0011.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Questions:

Is there = an equilibrium?

Can a giv= en graph be an equilibrium?

What is t= he shape of the network at equilibrium for specific traffic structures?

How good = are they (w.r.t. social cost)?

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Stabilizable Graphs

•G is stabilizable if there exists <= i>s such that G(s)=3DG.

<= span class=3DBB style=3D'position:absolute;left:-4.43%'>•Not all g= raphs are stabilizable

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0027_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAxAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAG AC0AgAAAAAAAAAIqhGOJGgu9YHtSpXNfdvhy7W1iSFplZ6boCqot+8WjK5/vCx3SziO7jigAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0027_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAz AAYAgAAAAAAAAAIfhBGny+0f4onp2Wup3rz7D2oIhZXmKBrSyUJpC2dSAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0027_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAz AAYAgAAAAAAAAAIgBIKmy+3fAkMU2mvrobz7D4Yih5XmVnXnCmmGy8aKpBQAOx== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0027_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhNAAwAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAy ACwAgQAAAAAAAAAA/wECAwKbhI+pyw0BnZwUWoqzsVd7x0GC8JVKCIzmukWGypqBQsbfTNsenusY T6v5QA7YkAFcGI+JpFLIPDifUcSUAWVesdWHJ+vbNsA28Zi8Mp+H6rWu7Y7B42kdOjOX3CvDvSQ/ sYTHJMhH6HdSVUikiCjVleLoBZliSIkIaOKXqXnH2YlEGfRiJRoEg2J6MKLCobrKWtPxGiv7aSdr UAAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

Connected graphs

•Restrict attenti= on to connected graphs:

•<= /span>Esthetics

•<= /span>Modeling

•B-connected graphs:

•

•Minimally B-connected: Every link is needed for G to be B-connecte= d

•

•Prop: <= /span>G B-connected and stabilizable è G Minimally B-connected

•

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0012_image045.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBYIJTAxMAJYl30YwQxmOsYGRiYGGTAsqxAzMkEYzExMkJZjEz///8H s/QYJaBi3HB1PEwJTAuEhIAsNTZ+BimG/yDFDAJA/gEgaxkQJwAl2YDquaFqeBh8E0syQioLUhkY CsB2/2Zq+Adx4QSwrSxMDAIhmbmpxQp+qeUKQfm5iXkMN+Z/Ln8IxAoKX8sdRdPWsQDV6QIVcwBp I64GRltBkE73Shifkx/Ez4LzG3lA/Ew4340BxHeqhNiv8J88+xkZQPQHuDseMCozgoImMwvdXwwk +gtiLjiWwO49zM8MMjdPIRXmg1KwDxXyYPx0PggfpuM5D0iHQkk+XIcxOAwUSmAqwjlBtqQV5edy wUTYQHEaAIwfBXjIBjKDdBkkYvERE8hHwZW5Sfk5wLAX5WLNeCpEZEg1MKaygIy4nQjjazOB+HaJ XNB0wgVOS+CAg6YSAQZ2MG8POPUxMjEpBVcWl6TmMqwD2cMA1KHI0AXRAAQtz4UY0EOTGSwDAEcg hvgSAwAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0012_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCQEjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQACAAB ARcAhAAAAAAAAAsIBQUIDQ0IBQAABQgIDQ0LCwgFAAsLDQAFCA0ICAUAAAAFCwgFCAUICwsFAAUA BQsFBQsICwUICAUFCAUFBQUFCw0ICwgICwsLCwsICAgFBQECAwECAwECAwX/ICCOZGmeaKqubOuq QjC8RBAUxqvv/H4ghURP97MZAwrhsLVg3HJLVvFoSxIRtllL0ADUglEiwxpG/ciiH3g5zR4cylHt IWquyyYCDtDU4lMQewAxgioLdCI1foYMWgJ3fykHY3Ejh2VnlZhYXWmceTIjMYiRaQykj5qlIoFQ g0iqJRCkii21q2GzuHh2rp6LrHeju4+uTaQner6mwCitlgyFyQG0oSy3uz1z2VGT0qLLk50A3ssp CxGxJpkj4ufpZgjNJs910TmTRogxRl2KTQHGkQDYzwu1L0ogFBQlIx8YfgLbYbHGcCEAhTYingCI xtSaGAMAahyhEBkJCZpu//US820dJYkd5VCZaWQeiXqvgkyyonDGhG2JAlCokAAkilpTLFwo5s6g zokU0jVRgICO0ROpSvyk1o5BJ4QsIESscSPBlKEJsA2Mpu4ExiptVxSxyccrCTWq9MT1NJKkILIz mgIFatDKsaMUa6AJFCfGV1jksGg5vA7BSMKMGfbt2gyviBiG7Zpw/IJdEZM7Sm4U7QnSRdeSXrql 0pIfIsIqTyH2Q7ipRyHYMtdFXXceUN/k2KpQVnnNLeQkud48cody8pY7SN9lnbxj1tLcb2L/HHCw dIOTw8vkfb6JQDU5gq+xTqLYNETu7wIxdzNmZOfWQBcZRdOZZJ8nBGrzhP9+aEDnWQvsuDXeM+ZV k15f2OAWkCx7yKcEfZ74Z9BtG4rHnynEPficehed1xUkESaXoA4K9fVdcVjBVhlxfvFXYVAW2oNh Yu0p1xpwFAkHYnI8AmVHHA+uNo+KAbJYg0b5rSUQaEoIkAQ6JyJI13Ci6FgXTTON+Rp/V/0Y1IW7 yYSMaii+6deHupXA3H3RkTIJj5/pSKUWAg4IzFXREYrFeLExWl+HMw4Ezwk/qLnmaknk8wAGCbh3 QAboCYkCooTJqAUEZGA2n3qoakCUCZ6Cms+pIvIVD4CEsmiqRHeQNRMyimmAgIjo7KWnDWZKas4k Y7axoCzIbuBEJwrh8FaIA/xA1tURA2Tb4ETneauBE1l4C+Wi6lQLRRuA2pMiudb246uZ2SIbpiTy DNIuN/z26++/JRwIMA/FAiDBvQMnrPDCPljGsA4C0HHAqw9XbPHFJCVxI8aUchDfZhyHLHIpEI2M Qi8CWGryyiy3jAkHxros88w0r8PBBhfUrPPOPPMac89AB11KCAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

The Box Theorem

•Given a graph, define:

•<= /span>

•And

•<= /span>

•When positive?

•<= /span>

•

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0028_image047.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjA4IKbAzsAJYn30ZwQxmC1ZGBiYGGTAsqxAzMkEYzExMkJZjEz///8H s/QYJaBi3HB1PEwK7AfEhIAsNTZ+BimG/yDFDAIg24CsjUDcIMbAcJENqAeqhofBN7EkI6SyIJWB oYERZPdvJtZ/j8FumACylImFiUEguDI3KT+HgaFFjGvhjCdCDDfmfy5/CMQKCl/LRcXTlIEOZ9AF quYA0kZcSxgFmUBaNSoJmbdElGsXbvMYGUD0ByRzd7KCjNCsJMKdi/C5E2IuI9zc21xEu3c3Ke6t 5CHavYtJcW+2INHu3UOKe+tFiXbvkgKi3SvHIkp8ethbQLR75Vj2Ep8elpLi3vvEp4d9pLh3Kj/R 7l1GinvbRYh2735S3Ksqhuzehn8MUHNBoiBzQzJzU4sV/FLLFYLycxPziHSvAstnsHvdKzmh/ImC IBVpOfnlMBWBfKBCLSsbxvfmBuvIhul4yY6uo5IFVUcjE0QHjO/GAOK7QfnLGK1FkNUvY7wuiGzD MsZSPlQbljG6Q9yQA1PxlB1dRSkLqpm1KG5YxghzAyQ8Ff6TF57o8dTAIg4Oz8xsGD+fC5UvyIjM Z2P6LYDKz+ZC5cPUo8c7lnS6IuOpENHxbgq2VxceJ8vB5eMJOL+UDcS3hYeXJC+y+mWMhVB59PDD ks4P4nYXeviVMGeC/asNtecXA4Svi83/FKX7hcwgI3Tg/rEXBvFj4Py5UHkuaO3MBa7BwdYyQNwi wMAO5u0B1/mMTExKwZXFJam5DMogexmAOhQZusAaQETLcyEGdD8zg/UDABfsXrmICAAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0028_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhRAFmAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABQA+ ATwAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFAAUIDQUFCAgFBQ0ICAUAAAAABQAFCwgF CAsFAAAFBQUFAAUFCwUABQsFBQUFBQsICAgIBQgICwECAwECAwECAwECAwX/ICCOZGmeYyOgbOue A/HOdG2bqh3ffN/nviBrJwwWDIeiEJFQKJ/PY7LGdEKvNym2WN3OGoupl8qQjc8osJhsRrvV7h6i HC916y8t/nzn6fdXfYAzf3WFaAMBAUgnCA5WXomKAQ9tWIdUj1uSipVjmDRzljqKjCaOkC5Mk6yd o6cJECirkwoIEWuqCaaOKygSpoG7BwUPA8HCso0JrLa4JMC5QUxIxcfSSkzKsM23awO+M9RTvSzR NQUB2yLRtJPbDZp2zNur6y/jIumpJcWvRQMeJBkwgUI4LPH4AbA3giEJf1ACDix48EpCbvXolYAj bpi+AApHQKSRiF+DCi8C/46K54mEIB4SWcSrWGRmCgv/lKjc6KBlwyY8af5wEK4BzjE7SbAc9VKU j5hpiNaQIFBEjgY5oVVt2PMfETmxWsS7tyTBVgDFsCmhusaRTxJfrTogy4PJ2bRj2LrsCuMVOLB0 U8wNNVjEgJDLzgKQEEAogAtqcThYNCWho3d7kQVh7IrdvXiKtqULhwAlAJsuza5h7BiyHQeab3Cm ZEbC58nqRDZuaBr1T8WsUbjeGMYFaFOWcefmGvvEPqsWIr8OxlK6DdsiqyKIfqqn9Rq+Uf2W4QgC rW3XFhZmLqZ6JsVDSctbaJb83PMj0pef3t67DacvYKePdty9Bt8vrTR3Qv88wSQSWF3ztVPgPD5x 0ooijukGyUh2iRGTI4y4VVlFDHq4XCj1FfHcgGZ0mJ92sCUholUkxpjfiTX8pUqESGyHjV1Z/WTK AA9KFkxw0LByIAocEmWUWkBCoRc7Q4IElycuDoDBVhnkUuIISIKpZFspCjHlYlWmslOWW07RJU9H 7pbkJAdyxEKTAjw5S5lirQfEFzbSZ6UJYc5wDloPaEAJlHyWxUsCvuQD5lZsIbDBmhsYSQ4zIRUq QpQAWHihY5IyEalHk05R6aVYZgrnpoOW4GlDdLRwaDGKLknfWyiUlEKQBoox64yEhePgirDoeoNv F50mFVfoVdLlc8Ptddb/sP5R+F2fRcnjm3rREjCtldVyda2c1kam4yzPhqoOstrqoqy8YqRD1lg2 NKuNs6QG6u6Fk2ToLiRQweurYQ9skOk+WCVWL45y0QXitkPEWnCsA7+oMFogNZzsw/eut2BxUVmx 77eZWYfvZj6tws/BJG110TiWvlbkdVtpU5qzkKw8YHEzPXMCVW24XALMe90cYM6x7Nyss+sUAzRR QhPaMqdHY3xKrTDIrAnNrkIbILobTdjrW5dB4uKnzJAaFosIb8C1XAJnAg9Rb+Zjbz8P+LLUTR6i PZnaqi3Yrhx+4i2jR3s/1LdcPumJsCVp/2bduvOI1lJAcq90uAnp0Emx/2QKiSr4ooaHc+jffANL w9OgkcYMbaCTZjbpJpie00g+wD6Z7J31Y7t0T9+opOt2KtXu6ny1XsSZeyrNQrkvuk6ogjekh8aZ +26G/Qzan8H9224kdd33X5jmAl48/Jma9PMgRkNa4r2h/oCjx98D/fOdcRLf+asL+agAFIDILzUH XAYyogEVG4AiR7KQQN2ecBj97Q99vYrgBHXCj5dICQkNRAcGVTE3sZBMCJKAnx1K2L7f1QFASjkh G3rnwjjAMAUyjEho5MDC9uVQLPcbRH4SKMQXJC8FQQQfEYs4Mmz8j4lDWGJKtLa+DZ4Bc1DMHhX1 YUXDdDGLhtkiWr4YB/8sgvGMaEyjGtfIxja68Y1wjKMc50jHOtrxjnjMox73yMc++vGPgAykIAdJ yEIa8pCITKQiF8nIRjrykZCMpCQn6Uf3CTEuf7TkGzHJR022gJNeeCAePLhHUa6RlHg0JSyk2Lsf CvGGezxiHGGJR1nio4dUqBoC06hKOaISjr184y/XN8JZ6FIkxbRh//IYzFMu047N7A4rT3FM+qgQ IKVQy6GwYCFePaF7a5SEgrZJweN5AZw9IKc7LlSJdeKoeKnpRjVZUKrPOc56BKyGMZIJnmeyTZ4B 7Agv7JkdfOJjGNbg5+v8KahaeOOeoIPYNh96NG86RFDXlBS8gsLNqhD/xCBIsahG/nnNfE5ho8oj 4xA8SpGQvuKiF6Vb7rT2xE9VE3rO4tUwU6IsnymBWUfxAk5Z95NpBiGEPClpVIoS1C0MtXlFTarV RnQayh1zbZ+CKlwMCosiTeybhcPfOcOaVW+Giqs+QGd3FPqx7AT0oIpxi1eY4i9wDTETCyQbCagn k8kg5xGX2aG53iorOtXmNoLlGGl687mviqk1XnKlS3p4nMoAVjnrIJYPZtMSAQkmsaPhjUxTliTI Bushg5IcoKiTrbVoTka32xVal8oVwmHpPrNDT4hE5izWzos41qElmF67kNiCKgjhmU+UyoMfw+z2 Nr4d3XEXk6DRfSmM/0plFyQk9CM+iaoVAkMWh8j6IRsRy5LXddc1bTnZnNQPTQfwUWJm249Yjfcs 5d2tzGrUIIjJq2ioIlK+/OWp2aCOEC3phWopRN+pgilNVyJP4bTEJS8RWK8GVgx7G9JU56knT7Fl m1lxJiwIV29XA2mTCN6kvDhVJMNkipyfvkgsoxFKry64VaIO3FYuoMpUbFsgpQRiKUx1h2lbHFaI lbJkHeeKUVv5Livc9qhTCVlVRGYVecI22H92CsdYhZnHUHQummgWH+06lhgdKwRmeetw+5ncuJzA V6xia0kSSKCAG5Hmd625ri3slhW+FedQSYsY5JKGncHcWvaImLDs8P9J45S3XnmcjKB2NR7AcHwj gm3FYBZL2MI6lhOi6SZkgVlw2XKir7CgTGwoDPVJMQYzzo1aAWOWlaT961NYQy0NS47wT7SGNJ5a 1glg4+hamGYelPguag+YmgCEplrz2bjTK3UiQw19bPr0iMv8eh6znTYfn0otCUGrzISsjTW4bNE3 s1pW/yr36GG7TXNm4FwJeTeNxAkgb4yDWDH8plWepILeKG5BOoIx3cwVNG77HjFh7vbvxTFi0gMi uMSLh3CsQjR0nZAGTpdBFt3thccpfbBlvUlOGvashg31ZgGGpxUxqPVfhiVEKxII77+ynK3Kezm6 aCFzmqfqJyVvxYiWWy6TJDLpt9PDhvlQZNReAR08QWRfEafekaof7eqvyzrU98TKCnb9B0K5eR7A zj+v66CDBXzlAOcH9LaXEe5ub6Zw0yDZPS0QhGNvLwo1aEMWbliogA/g3lNCeDfQ8vCzwGUT8+V0 LfpXiTWBORpsWdM6pLAHZh8Kp7fA+cp/cprFzoNKr2BGOaaei3Rs/SbFOHMdVCQEADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0028_image049.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBgjQSeBg4AQxCqsYQQzmi0wMDEwMMmBJViDmZIKxmBgZoSxGpv///4NZ eowSUDFuuDoeJqCZOkJAlhobP4MUw3+QYgYBIP8AkLUCiA9oMzBwcAD1QNXwMPgmlmSEVBakMjBs YALZ/Zvp0Z9qkHUME0AkExAKBFfmJuXnMNQ7AAU+ynEpqDAx1usCscIF5noGBgMGFqC4LlA10GAG I65fTE+ZQVo1KokxT1+J6xx28xjB9Ackc/9xgozQhJrL8BcSkDjdqYjLnRBzGaHmhjGvVAEZ8bQS xrcXgfAh9jTgtQfo/vPEuZ+B+bg0yAjdShjfkhvEt4X55x8B/ygR558HjG1MEHvQzQWJsgDNDcnM TS1W8EstVwjKz03MYyDO/fPYFyuCTHCHun8eq7QCiJ8F5S9gnqEBSoqZWTD+GTlGJP489pfCIPms bBjfUhBsHozPupGfEUl+AbOeBKp5SXyMKPz3jBA+ejyR5k/08GNg1lcHmeCUBeNPlwXxE+H8o2Ko 8rq8qPIP2ZH9ycC8hAXZnwzMv/6D+OHZWOKdrPjhhIbnanlmUHjkKaTyQENUWwUkV5SamJyRmJST ClPJqqwI0puXX6IAC/vV4LhUyIfFzU0hED8mH2a2Iz/UbAWY2QeFsZu9UwDdbEcBiNlY8hNF8dTK BjJCJ58LWppxgUs8sLEMELsEGNjBvD3gMpKRiUkpuLK4JDUXxONiUGToAisGES5fhBjU/jHUo4ct M1g/AKDvB4a4BQAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0028_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhdAFIAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMACABw AT4AhAAAAAAAAAgIDQ0IBQUICwsFAAAFCw0ICAUABQsLDQsIBQAFCA0LCwAFBQUAAAUIDQgFAAgF CAAABQUFCAgICwgFBQsFBQsLCwUFBQgIBQUFCwsICwsICAECAwECAwECAwX/ICCOZGmeqCKgbOua A/HOdG3feK7vfO//wOCpIBPeFAajcslsOp/QqE5RlKaq1qx2y+16cQdEAqoIBBZjEwOx+rrf8Hi2 YDY3HPWAgYE3PwB0eWZJJAWEahB5DwwRaS8MEGgifFglhnJLA4KbdRJtJJCbkpiYmpybnoiijkAH DqOao3yjM3x/JaGHuTWQsAG3JwMSrKQ/prQlrsAlmkWuw8Vyx8QjyijNIs/UPK6HdFUDhzQKqSTP n5MQy0fQKNbRQdPX6yOawGWV8F7ywfQi9iPwCcEGwFQRBhO2tSjQbpKDciVU6IAkTo2Divp48MNF AQVDRwIzvtkIquOQhiGB/wBkUKHMrQL+WvRi9Q2FBYXJ8IxSxqeOuJk+ei648BAnF5Iu+Oh6iM6L UKINR5pBlvTiCD4Qf7gEQGVrOByzHGn7cekftDXUIEXNIfAABqukkLIACOAcnLZvMbqRe+1XNqZG GAo4kFAwWjBwRZTRC9YBsAJoDiPKWuZUgHxbRdCJudfMWo95qHrJDMhvXM9GRwSamloHwwsVVnyE maNbocuW8nwOVo5SGIVqm9pwheUjPFO7QUUaEyrfFuKFkncOID2dpOZG1FIBoJ3xC1eyEvmrSQNy GmEZqAOHkPWG+avL9YURbgK6w/ZaLeMuRAtotPnfOVAFVvTtAEkDYnAHAf+CxPjHQliq7QdKUTRQ EpAedE3WmjsCkkCQg3DQ9gI5n4Ryi3/GOWHfP/uB6IaILpAIn2koVndCTyfiwdkj8bGIkW00vENR XR3e2KNi+mEhTInsFXiXc4j0p+MXS8KHXxzb8Silaa0kBuQOKSrIJZI7RtSONTMxYNJVieFAjiN0 iBbHVzN8ydUZGzbxZoRyjuRdTuKU0acOv1WTYETqzVAlm1yq5Qh2iByyKDkUxJZTmS2sJOBFKpRh oxWE5blZOtS14ekYceapkV+UcCrAqXCEWh6NiZQDa6o4xOAhlHQ+4pgJlXWCTk+frfgekfgJo+oQ qLmyX69uSOaCKZtU0iv/ElIEMoyzRUDr1KHTnmLtIdg6AeMLZeVwE7BXupDuEuc6ZSkLBzjp0Ynq hIgpFCzZW697+O5rIBs1FApGPkPesIa9PSysrwsWMIwLwdxR/IXDL5YZsQ0YY8zEAIOekCUvR5q3 5xFQqhSyFCN79KmHsKwcBcjLLtHyScvS/I/MPNw8Q7xuDlKbBk/4vAW1+uFpw8jvjpayFEjrx3NA VTSdXWwS2bDxUVNPhLXETUSt359qfG3LG/1mfXTSeZCNi9m/NtHT0yIxMXfdOdytLNp40I23Rbjt /ffghEehQNeFR3N4zYk37jgKkAj8OCaRT2755UmxsTjmIi28Oeegc96T/9uhX4wH6aWnrvrqrLfu Oo9uW3jp60EkLFOR5sRNezRhgtWI3KdXJSGLY7748o2/2x387cMX5Mfuq8tqbuwQ5PPO5dI3YTUi 1usOfejHak9995KLFD4T2+NSfX3ef/8GrvAZ4Ow9dRQRbEWQLYZkos4/T3w5hpgf8VhVPU+14XqV OV4Q4Kcg+U1pf/u5nyUWoL878Y9awEBOGwL4QAwqiAAG/Av9+Oe+LZTLIQFoQGEksTlNJGEDnyNV AzSwOCIoKDK/es/iHAUIFSbAPGcDIgQwQAAevsOGLiLDUlK4wjG0UA8AgCEyQjHDGsogTTlkYWTY gyofAjGLCYAEEY0YN/8kHqmEUqjcBJ2IBgSmIoYBOdOh7AGgN52tIKnQYRsJZkcIEMIagJxj8Z6g RtVoMQFuXAEcFSPH8/yijsO4Y5X0iEg+RtKPIiTSHwyWITRGwWOqIcTiFuW8PyySK74QRNXUI7hC iJIWdLjkQTpkDbH5TQigBMQrE0BKgJzyc7aM0DBaGUrFwFI9kJilDGpZLU9aQWeW2GWGrPHLmFFj M28iZTFRiapf9FGZmiwI4owAzW2OkkvUFA0wRYPNYeKnLJtrZxjXxx1a/qqczpyDXuDZxsTsrZpp AJCHoPGmFf2Ln7wkqCyzQbBAgg19GEHol/6pzp1YzCxO3BbuDipNhc7/0xkN/ZVA82mFO0bTmN38 QzJRuoGIwLIdCniAjIwjGBGsC6EzXWjCjgjT8jWsfbpEaWlUSs/FtZQEMUxRTHOKqnLcdJdMXelO y9hTkj6BmJoZRGVYWAdgCDBCJFzNFfuAgVKV5nmBMMBWiWKGsnrCWS3qw0vqlwWspnWrTuxqNR6Y 1bDStScBcKts9HrXqbA1sKWC6yz9J1arFm2cju0ZZCNLWZnkq7KEvCxmNwsWzU2Ws5l71WdBS9nR kVYJpj2talfL2tYW43o8YMSGUvs92Lr2trZFVx3QwAEn2ss4K3VfbnXLmt7eVrWxCChcDnDLij2U pMn9C+qO68mUKOZE+Mmb1mihZ12u+JS6lkOTH7+61x99Qm23GQURADvd8P6KIuQtb32eC17LmWIR ePAiMmraAuamgBAOW9fu7tsT/RKDv/X15BEPySZaUKsdskXELX4DNNctmI2sgNAAFZjgxx1xl2yq iO2yIRyMHe6MtPuwUEOsvvZ22MNlBLFDptg+NcHgOuzJQLtYp2JuTojG331x4noMRwTjkRoC3uZ8 TLo7IlPFyFgVcuqcnGHAaEY0A1iGJCVhCAYQrckxXjGbIHI+KZcOrg8orNJuo4gbfRmjmukWCS0s VzWzUxBBNjNmT6nnPru2kH4O9Go9t11BG5p2tD305EIAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

The Box Theorem

Let: =

Thm: G B-connected. s is link stable and G(s)=3DG iff

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029_image051.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjB4IHiAhYETxDL0ZgQxmFuZGBiYGGTAsqxAzMkEYzExMkJZjEz///8H s/QYJaBi3HB1PEwHWB4ICgFZamz8DFIM/0GKGQSA/ANA1k4gXiDIwFDJAtQDVcPD4JtYkhFSWZAK Mhxk928m1n+PwW6YALKUiYWJQSC4MjcpP4eBgUOcq3PGEyGGG/M/lz8EYgWFr+XfxNLmAQ1k0AWq 5gDSRlz7mH6C3atRSci8g8JcFrjNY2QA0R+QzJ3ODDJCs5IId3ZFPMbtToi5jFBz9zIKcRDtXkvc 5qK7dy+jBDeyexv+MeB2b3fGU2LdG81SzQoy4l0lhM/EDOG/hfJXMkL4b6D8/8zm/CD+eSh/PyOE fw7KP8DkzwLi20LdqfCfAbf/rXC7E93/woxZ7CAjdDH8DxIFmRuSmZtarOCXWq4QlJ+bmEek//8z 5wuATHCH+0+ZD5QFMrNg/oPKw/no8jXgeEmG85W4UOXrOFD1u7OB+G5ZsPBKZUKWP8BkxQDi52ah hx9p/kQPP3mmIB6QCVlZML4TOzJfgdmNEeJuLOmLovCV4wQZYQD3/zwwXyeLC1pqcIFLFrA1DBC7 BRjYwbw94LKIkYlJKbiyuCQ1l2EeyB4GoA5Fhi6wBhDR8lyIAd3PzGD9AKkT9bogBQAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh/gBFAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABgD3 ADsAhAAAAAAAAAsFAAUIDQ0IBQUICw0ICAsIBQgIDQ0LCwUABQAFCAsLDQgFAAAFCwUFCAgFBQUA AAAABQgFCAUFCwsFBQgICwAFBQsLCwUICAUFDQsICA0LCAECAwECAwECAwX/ICCOZGmeaKquLCkE QyvPdG3feK7vPE4EhV7KEBSmDgijcsls8hKKpBNAWDCmo0Qjhu16vz2CA2t4XL8JiBTMbrtPgmJT ywVXz++8viuoM+9tCRF+e4WGPH0nWgGMjY0SCIuOY1kNlCaSjAMJE3iKEVYiWqEjAqRggqSjnjqZ MJysh0KJKD+XIqaxJgaDmA0Bl4u3n6oNp1SQgaBnq0+/wc+yTbQnBzAlBhQtB8kkvN2VhDi8ctLj EeCiW+ZL1CYCEmdEAAZrKvCegukjSD28w+xm6LPHj2BAHe5ICLp0QFwKLfFcAEFRQZc6TfQiBDgG INUZawEiLpEUg9dGiy8c/+3DNfFExYOzHFK5Rk+BRWJ4vt1kwQ2PAID6GHgEEMdJz1IAO/ZioRMm H5kpG3FUweuUtaQytARbqrCBBAsRKBFY2UNrFq5Z1Mi46vSpImMfsaKo6rNlKZU3edUZaxAiBJFk uPLdpU3Gi3JE8bZF6PDfiHkz6F50eHgFtzW5fEmIgNgouMwlQDpitG8RZbtLIK81uCOhCGt16tEI ercz7YdwRXF+i7FLM6Wdqch9h1o3YCWABK4z4hrizhXOR9jaFRb6bhF6P10gO/J6xsY2ZUzHVp1J meeK1MakPrwma1zgTIemmWLw6+Nnt6/Jhi3KDvsAHOVLcLwRAhsTdPgwFf8OrlWmw2UKaVRHdBeV YwoGZph1Ai8ZLEPFgogsgKFQlgxRHguC0EchciCiiFYOgmhAwg+PWPTbhi8GOFo6KYq0SETk1AIJ jcD40mILP14R5D07vqejSk7CWCJvjWzSiQtHZhWBjDccQKA67anwUjXcgaaCl0tAuBiO4ghTSZEz cjebejZUECUy6G1IoIa+yFSCnUrwuWZo+3xDUILeeAcjnbOZAd1yynGUi4AmJKdCAo6GyAClg7pw 3EDVEOTYDmncWUuY9GS6A0hyldqCGEKwqkdKMbA105ErJkbgmGdliaJ/NjQkA39fCLuNn532h0Ac +IjBKSYeYodOnsZR+1D/eDWkYS0BXxqBJpIQWDvoAQs0BNEG2sATpWSvwZmVV2uINhojBMI6J7rJ YgIBvvmyIMAF2qTSyVAmnuLgXTV2JSeSwCqHX7659vuJoz88kMSSBTPzy2m2wZvDsxKHPMUPRdiq 5kPT1gbtwxFr2a3IMM8SUXQtl7DieIkmRfCT89JrwskxBy2EhqMu1IK6bxpIX4SoXtqw0FDnkN1M XJCcKbkMGNAw0ClO6JUuGOdgb9RkBysSPu0+TJ048ob0HoAwYlv23Ev8IGJuYCLk66+m0u23crUi Npa4XSErEKN/J36D1lcAWriChKPgquKUBxsEprGcZ8PkTyBe+ecPqTU2/zaF0WBsDxzkmIdJCztF 8I2k/lIlLJGhg8Dplb4cmu40pG74F4NNDXG0sOPg5kVN2xxuW5zrIYgcICf+LY6lQZrVvqXD1Hwe J4et+PZnkdXPbF8vBn4geCuVvCEkZXQSCm2TdfCfkXd6Phs7F78YpT/h1JHn0lIb5e4HhlGpQ4AH 4ZMg2jSlAH3JVqBLS9+mYMCOlK9TwoMbdrAFhZvMLzEJoxsB0XAipexNFiczk3Qu4ZqkwaE4ZRuh F25kNPvh7XknIFKTiGOblP1Nhl6glPDWhENpNSZgAJyRux5TQhEmkQ0Yix5MABS9Uo1Ochubz+9i BsQgJuMHW5TGhTLUQFDqIDBCKrrgD5/YBhqdMSBJyki32ua2I+zwe2yMoLfkZCk9zmmCfjReGQM5 NOsRsgeTeuMhLbdIbzFifY1sAeMiSUmnAK2SmDwERACZSVmEAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029_image053.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC6WVT2jTcBTH3/sl3dq0a2tkptYd6gZjOudB8DIQCoKDwhTcYOJtlsoWrBU2qLnt 4EnrHzyIePEiyi7qYR4EkY1Kb0486UFkMkUQdYIMBKH19375JSTBYIqFNO+T33vf9837pc2bl607 ID6rOYhBgqLXR5EC5YkCwGBArMb4kWBOxBBlhKzT6YjoIObktaSbl2IQW83pPBruyUAeOpQMWerG oxV+LPGiFZXXyJwUTM4uzk1bFyo8D6n3bxZrbwoPN6gpUxlkp6zqmdo5gLSh5W5/1OHt3Z/1D/wo FLbreeNsgwvCGM+O8/Mh7T07zah0xPqXnmFoV8L1EOj8w6P7SyGJfVYEn7tPbYb7tHVR6q7hcjyy 30a4btDvGj5KRvab78bveCay36vd+C3qkf3uie4X1efJyH6vRfeL6ou01+9SG8L9Dsx9iup3WH0X I4kty+Zbkr9LZsy/PqjY/E3yQ7T5q2RFHd1F/EpyE21ed/lEinhM8gZ7rBIfkfdV6ED4vK6H31dw XjOKLvZhVPYx8Gba29dAjNscnCddpb7T89XKQuF4pV44WavOno84T0UtG6Qw4c7D6Ke/rHnT4RHx PJddXu/zr+8X85lweStBfMx05if1XfbrN/Ge7tVvYmmHf/1+xl9f6/PrP9X8+f0Jf/7FHuIZ09m/ FvOub7AiEE+awf3sbq7B/SyrbeHbNB3+onl5iJV2osf3EBtP+3m518tF5QHa9/mX39N/7X9JzPOA O69W1s+HNZs1+VbSxJtLtAXbSxZ6BT0T7zpkbHDKWlisVKFBfYFX7IXLooC+Ln3WITgzRdT/AQCi 8wiABwAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYAFIAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgBZ AT4AhAAAAAAAAAsFAAUIDQ0IBQUICw0ICAsIBQgIDQ0LCwUABQAFCAsLDQgFAAAFCwUFCAgFBQUA AAUFDQAFBQgFCAAABQUFCwsFBQgICwsLCwUICA0LCAUFAAUFBQsICAECAwX/ICCOZGmeaKqubCoE QyvPdG3feK7vfO//QBYhUAiiDEVj6YBQ6pBOEjNKrVqjCUXTSlgwrIlG7NrqfqvhMXnNbqsIjqvh cQZDtu7SvI6+5/+AVwJJVGlsZoEAhmuIiY6POgkRElxebJJqf41kmJCenzKSlCQvAaYTEaamDpKq mShhcSdhqjAJFHwmkpaKDbwiAr82tLW1FXiwDbK6DbUDt7klu2dhwsHRStMi1dg3xKbPuKBGoiYG EbxDvNq9xcvnr+3LtMuw6NS+fATHO0P1ANe+rRoBj1mAec3+6bq3LR+JfciwMOwlDAe9ERfHBSmn J8KyF4TgzDjAj8S5khjF//Q4RwjHARh6LLAgGfFkxEU7WGqcYVOayp0/OD4kImIIUUV0ZgiowEcS SikRcZxTWGPpGSgGopqwSsKp1ik8pgJl4fUE2LE8hI4YEiMBhJdjBMRLEYYpqaMmLnRrB/NcgIrs vHkccWDurAZ2R4BEoZdus76pAE98GSBxD2Ix/FZUXOwp55YkGqNNO8kEXAAHCpwWOSPwyb0zLQtQ 6BT2CrYiDCiwjXEigNc5SNaZvZCptkFBhCum2okF8NESR5E6tmcpgiy8Tfp+STWUst7x6mqVUUrV 5iPbD+aIBZ5ZBQyDAUAEwn5bhPB+WnCHXqh0iaUZ+GGVXDWc88tid6limf85963lWS8PesfLAd2d YOBweAFjzF4FFfVgXRAsGESH8j1ogEzkZQjQhvyt519KFaQGIYU2XNgQTFupaBpK17i3BWXFqALa b/H9NmQKNrYzF4Ip0KTYZnVFcOQPTgKzGZCd3dTMkjq2SINavUywW5hj1lDbZ8XBxo19R9aVnVk4 /jbeLBHIpuOZjq0j5WHgYOGQInuawFoLTPYmopdfvmgfjq0YtoKba6nXUYVsEtTgQueRhdib7tXh D4OUAkoIiV1FMEGEPkgy6qV6lCmEpNqF+gMUI80pmHS5FSmWOa6iYF1KcYpw2hsoKbeQrOh1p5tt v974yrApzCfsoYCeisf/iQT1aoO0qFEbxpQGPRtsFJu0gBNpuP7m6rLBPdUojHXQ0lIwGdBRH4Pg rlCoDVUuqgakN867QL0M3NuRBgyVywO99n6XbCip/LupFXsMkx+6JRDQksa+UqtdPFhWhkwridFi l04ncDuDUaYcypUKpAqbZamV4VMzkVNCxPI/L3vTzMmBujAzCiGjSt9P22ZqpqIFoqiCwTWItuN4 PRqB7aMO3yD1EqhWfYTTPfSL6ENKP8qqDhucXUNhZXi8Aq3MdHcuEGwL4TbMU0KdkqPC8m1m1m0Q c14rf+2l942uQENK2TKk7TddFz+NtIS5XGOsoIxbFLljj/tUkeUeKyzN/+Y3gM6pEs/9dzPMassD 7D8q4+C4VEm1UDEPlFXolq1P1O6c7zrkDjnvtwc/UCJDPGhUvtPWVKeWr6CMdusyQOsc2FTUrYT1 b2MfhfZNjjt2CRdw4JkBHZjPO0ALlmWa88iuMDsZHFch4yf1Z8/8+OY+YL1bHvBNMha0rxFsDVCZ e5QW+MfABu5EY0NoSWFesj/X1IlTeFqPthzIwQ664QII+FRRCiAe56Qnfg15SsiKcaRBefCFMEQD LnaVAHsJED0HUlF5VpfC9T1tgTEMohCBAIVp7E4+XWLQOrZ0ggKW0CV3G6IUp7iCKbipbs0ym52G lEF4CWZ/VAyjGBUhjv+6eABFgZGcZUQYKzoJY4W1AI3YxkjHMV5tRYmJYKsYoBtkZJEW4pqLJFAI CyBOEW5OOEsdE/EtwpREXiNxV8S8iC8euFCIotvI5BaZh/LYhWMC4VEFMvCnXIFsaIIy2gzmxz/F WQh4WCAdJ0eDrfw1hJBbSaD8qNciV/qkcz7I5CyBwjYQpvJ0Xdmk7HjJH1+SDZmRYOYwQbE77DAD mJiD5glY6QmBZMmb9TgcX8DhTEzh40C67CA71nSZx5BTHDfYwx31AEtzyfIG3MQfrKwUL3h+zCAI 2acbz+kpVcZwnaVcT0JeFxwYgC8m/MImC/LpCe7Ns5zdcp5n5hbPoE3/Uz/g6kkyJTqLe46QBvfz AUUh8TKsjMyfimnf88ziw7cV6aOPuqf7llDTWTzgjGhZqSMGSRhsAkxDUzpgMvukmaakh4fqfExm ItONommlgCJQamsmNhahIg9H7ILYL1LHL9n840zHASOiLkcccyrinmTlpFcDscPC8eSECp2H2sRD 1BL1tJlZa04yl5FS0whUrtL8AztpdNccgmaHbiNR7MRzOSFK1kRlsqavdMiiKc71D7syEg2SBMgm JtGRePBaCuGjVgb2S7VF+YijSpuj1jbws3mAVlYStcU0SU5PXEQM9w76J1WlLEgti4oTLyhG3AaO qz5b42FDa49VhQcd/3M8aNBilhuZHPEN072pZxPrBupayJBbQQltCSO+jBXrUIPk1jzV9VdQcKuy GLnDJfkUyDE6lw1YRakk4wQwSC6OYIdjiTaEyUCGFQxwHYmivygZxv9egWVQTabSuGvV3vDQZF+Q 3kP4sTNmpJOaPwuxRw2LShYrqL63Ja9GbBk3HGi1eU1MII0bmN21nBinFv6EMYkFTUT6hDnKZAyM dyJOnOYgyJDQLOe+lFB+4rcoCZQy/0znZCBA+RHzPUI9byC8ktY0zGMrc5eDYlJiAhPNRnioCuS8 5jVzFC3fLYNtydzaPNf5z6jZcyBqCNTxEdp7gO5yWEdzVEQ1OtF17g8xpCdN6bQgZsmVzvQOQgAA Ow== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029_image055.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjA4IPiAjYETxDL0ZAQxmHcxMTAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgesB0QFAKy1Nj4GaQY/oMUMwiAbAOylgFxgyADQxsbUA9UDQ+Db2JJRkhlQSoD wwRGkN2/mVj/PQa7YQLIUiYWJgaB4MrcpPwcBoYZ4lzSPx4LMdyY/7n8IRArKHwtXyyc5sMCVKgL VM0BpI246hh/gt2rUUnIvKtiXIW4zWNkANEfkMydzgwyQrOSCHfK4HMnxFxGuLkbuYh2bxEp7vXn QXZvwz8GqLkgUZC5IZm5qcUKfqnlCkH5uYl5RLqXgS1aAGSCeyWMz88HSgKZWTB+KgdIvhDOr2QF 8Qug/APMUP1wPqr+A8wZHKjq3ViRzWtgNBRAVt/AKMuNbF4D43Swfl84fymK/Q2MqUyo6q0YQPzc LEg4KfwnL5zQwz+BTZkT2Z0JbOZsyHwFFjVOVD4LivwDxn+cqPxkNHk3RggfPX6xpEe5jKdCRMev Mj/IiPPw+LNkB/Ft4HxZFhB/MTx+IOrPwfk8YPW2cL4UC7J+YPizI+tvYPSEmofFHxSEPzBdgvOr AcJdKPwGxsdgdytkcUL51XzMQFZiTk4qF7R84gKXYWCHMEBcJ8DADubtAZd6jExMSsGVxSWpuQw+ IJcwAHUoMnRBNABBy3MhBvRQZgbLAAC/dXdxigUAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0029_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh/QBjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQAAwD1 AFwAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFAAUIDQUFCAgFBQUAAAAABQAFCw0ICAgF CAsFAAsFBQUFAAUFBQsICAUABQUFCwAFBQ0ICwsLCwECAwECAwECAwECAwX/ICCOZGmeIiSg6ECw cCzPdG2Tqu3efO//pYLhYEMkFMCkcokSEmtGJHNKtUEWzyLjVe16WdcsdPste6M+p3ldRffU7PgP zkM0pPL8e+iz48tGDk+BYnokRg8oRgGMAQoIEWISfIZLiwGUJXaMmSeIigmNjpCSnV0QDQGCAKiq hSJ2lEamTKh/sKGJuAG6IwUOXJVLqKsmEq4ytiaLvcxBwGuEuMWaDbIJtEsD0DgN3CNuI6grMxLk euYsBarBvoznMNvtrN7z4SkN8GcJxdLCJBKoAbDzjcSObr0UpboVbSGMCRQKsqoQcR6KgGIIWgRw UFyDhPv68Xt145gjjrxE/6zLBm4kwAD6RkwoFIskPYEn1mE6MIARyBrEbIJb0PMPAgYWrAltKfBY TBEzq7G8sekd00EuD4U62YolhAsEzGEs8GDb0poeccIg+Krn1GoCEqxY9zTezhkFBNA1qKBnXalZ gkLxtpQG2mNS/PkrYXaEhJ8jBhgY8IifBQwAAm70mKknZBaBgi3624QdrI+GQ5E2MYHAul55Q89A 1TklFH6bi6AGsHdg1sUtm91hISED5liR0IJR6hhmCZOMBMrG51zHydOfTbRafSgSKl0IsCiPQTuL 0+eipOOm0rO64qzd8PzabAcL7wALXowjz9z3dfQxTWeQbTLMEthw1mWHw/8KNR31Qm/J9LcIQ5lV p5VEP3jW23tqyeMYS715JoKHaxHWXIAmagJfEMjAoIxjauHVYgsvEEKZCJoZlmKFKKoF3A85bvjb ir7Jkg9xq0jz4zLwvabdboCV+J8JjeHDnZQUkuKbA5ed9taFWThZwnee9AdEb0KKhJMd57zIpC5k DgQlDDnucktRZSoI0FOf4KJnDemMiRmOLUJYzjcTMjYlOHNmeF2aWOE0X2Qx0iPFOpfCZN9XB3zV Domn/bckPVeWCN6cnHqqhBHnkDiadhd0CpZBBW2Cx6j7KVHeJgJocACHhUyygXgJZFclRiPOuBxD 7TWCoUoF6SSKKE9Jywj/hTFYO62FFUZHRF7+OZvbmAgOmN5mky5hEpepPFDVKKlc2xIyuSYR0AbY ZFQsEJMUJkO/SOL7pRn35qvVn3QOLAyoQECAGbjP+AsKtoOR5jBvpX5xMcQk/CKxJ0f8E0OfStzY GpMUZ6twPM9GhsTJIpts0T020CEyQENUmYSDCMR6Qhh1kPFDK1Z5skXPH59xtM/a2UeV0DcrSqCu WFyMgtU6pDxFGFgLw/WgP4Ndw41Rx1EU2U1kzJHaQJyt9Rpuw8DxDAOwXfbOUN8d9LhyOKj331As 0CXgRQgutjDhDU744qBUyjiTjvdN5OOUV2755ZhnrvnmnHfu+eeghy76/+ikl2766ainrvrqrLfu +uuwxy475a20PPvjyhloyVbXamnIpG7ebnnuBgPhzC4It3HkiJEL3zox9oRsCKj1Oi+7Rid0JHkm diRPc8fvYGqGTjn7NPolSHRlE3TRWXTeCVHpMZ7uJbYsjQURJd1HPnLdZzfjOntMmd4mGL3FaRpC KeBF+tEou2yrEX9ZBze6d759nYYhfpOBiP52wC2RZCWFEZ9KFuUFPGFndG5KFw4ORxxudctb8pvT eJKFsPHUCRDFs9ToQAUwqW2rVqGg0Pvkl0MKamVq6vhPedYQPGSFjn5syknyhsio5n1BZ8ED31sC 6MIYNOuBdcHi8p44xv8spoBp2UIiPZJ3ijHq7Gc7YkwxClAB2zGBZCQLnQrf2JIrJWpAbyuDh0Q4 snqYQHwDeEAPUzWrO+7GiGeUFd8IJyxiZaeDoHEIAm+mEytqhSEmEUAU16CtQGJuEauo3gnYZ5rs TcuOolNhwVZWjqnMUn+EY5j1fNBDVjzsfwqx2C9Bl8dd9qB6MpuCLhnzskkurl98NGYNrAWepeHy avHqIiys2bn2sFGaNPiaHsQJznKipC+mZELczGnODMovb+y0XuJYGA3DxROcozJDPu/Jz376858A DahAB0rQghr0oAhNqEIXytCGOvShEI1oEmrnTIkO5hq0XAvvRhGJSgD/r1wW3ZmEctiHXMzrm45s lSdxBMyQsqBu2JTI99hAvTFmkoQuNR48T/Ms7cWBfnJSkAKTuBNvrkp6hwwfTjeHPnrcxZXnMoY2 ARC/PMyPpJF56gzY1D9DUcWQkCMC/lZquQBCBi3u7AZZ2dBB4LzqBhLkAiStEMfnMBCluLOgnDCo V5i6Eq9maOuKtsMDEwYVrlrNyX8IGboUYohTsEAjgNDjrGsaT4ZmGhAbgWrGl6pxGWa6Yeh4SAuy OAZbf5ysIYA616RasYkrPZ7clJjZz0HRpu54oESoyFPLlowana3GUpl3ILuB8KXU4K1tywhScRxn p+D7CSbzUK9oEqcusni0ICOdOVRKPYGO39ju5vYYIweZVqOLMmwlBjncr54KsNWQCCIVmVHKVfJX en2SFW11FU7CMKkPLBqAG/GHW1IFqYSCyShx5ACB+RZxoUglbn0orha8sqKc66WgMNYFFfqSw6Bb pi/q+7oFU6mZXdBwMm2bX4KKeCDcpEL1eCbZzEFzreAkmjbJyQRqiqNq9LycUUO6Trg5Am05JSZ0 v5DWJHNunn2zp5NZjOMf7POfIQAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

•The following are equivalent:

1. G is stabilizable

2.

3. G is minimally B-connected and

4.

4. G is minimally B-connected and

•

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030_image057.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjA4wJfAxMgJYm0IYmQAMpiFmRgYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMCUwH+ISALDU2fgYphv8gxQwCINuArGVA3MDHwMAGVM8NVcPD4JtYkhFSWZDK wFAAtvs3E+u/x2A3TABZysTCxCAQXJmblJ/DwMDHzxU944kQw435n8sfArGCwtfyieJpk1mACnWB qjmAtBFXHeNPsHs1KgmZJyXO9R+3eYwMIPoDkrnTmUFGaFYS4c4YfO6EmMsIN3cqO9HuZSDFvcac yO5t+McANRckCjI3JDM3tVjBL7VcISg/NzGPSPc2MM7nBUV5ZhaMz8gBMtEdzq9mBfF94fxUJlR5 KwYQPzcL4i6F/+S5C92/DxgfsSG76wGjGyOEj+5/Bgr9H8gLMkIhixPKf8nNDGQl5uSkwkRucoL0 pOUXKcD0tILjQiEfi1vQ45gp4ymxcdzA6MkCMmJxPhc0R3GBcx3Yi9D8JMDADubtAedTRiYmpeDK 4pLUXIbJIHMZgDoUGbogGoCg5bkQA7q/mcEyAFJAm+w8BAAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh0gAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQAAwDL ABwAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFAAUIDQUFCAgFBQUAAAAFCwsFAA0ICAAA BQgFCAsFBQUFAAUFBQsICAUABQUFCwAFBQ0ICwsLCwECAwECAwECAwECAwX/ICCOZGmeIiSg6ECw cCzPpEqL7q3vfM8XhoMOkVD4jjqg8EY0Ip/QqAmyWA4ZL6kWQLUysduwWNb0KcfIcu+MbqPZPETD 6d7Bd3J6ff8kOpAPQXw0foCCJwUBARFZW0QRS49eg1xzKESKigoIEl4FjH0JioclcqOTNZYnmJmb nSSfjSQDf4mQWxANi0K5u6sNh0SkTwOgpaJ/IpjJI7krULm3Jg++MMWyysgjyyXOU6rFqKHSkr/B CcOA0s0NxttF3Q3MMQ/PiIvYAIkB9iwP6ynaYVPDbp6IRHrElAOwkBLDBADluJs1EJi4bboSlphA YSKXCh3zHYso8EQOEnLS/yF0s7DhDWoBjAwIkCxRulIWSVDrR2LCJIkXo13ctmCmHgQMLOSEkdLL ThQ+ca7rlYkZTJqw+NnyYkqRvZYQf4qKWSkAKQgXCNT7d6CAg3Awcp1tN9TEo3wzbyISkKjfAAUz eZ6Qa0UoE4jYViqTd3AXqwoYrmEURM0JWIAj4Ip4MG+Agb+PLGAA8E8kO1IzDca4+46fjgkEEjEr IIB1DMKZsR72qJj0utSNb8qp6fohubB2EzDLozPD6JSdmsZdSrr4iKvVsrnrJZgFpwO5kiGoIv02 9ac6M2U3npgsQ8YYb/WNMbP4ZVS56MTCWEVfgAUveMMUXdm4VwJ6KCFXAv9wMtjQFFIvzEcGgQ8Z mJ5gLvnnRHgJgiKhSTRJeJ8Jkm1GioQMluidgtVhSCFK1JWwlTUvSPLXZh5dwiKC8aFS3giKyXag h9YNGaF9CmYoTCQN9MOWcUJkeEJpQOqWimrvYQmjhdu8Etpo7+k1pTtCxoPlcCYoZph2QnyY1TMi JsniYvbk904yHGY5SxBoNaIiJgkZNViTNNQzBZjVSeNmZnymhYM7gC7IZUCC9YagHHAWmZsTcR6H 2X6PFqZKkPz0N91RGb2D2UE5HmZPiZh0h4KdGBkopT45CrqYe4EssWhAQZgigAYHjKiTARuQp9ws 0jwJwEyKmrUBOlYUIqm/eq2SNsw+6qnnZCbyrcCKIhPZNO05qtUHrmm9btlKgV7ldso05CpFU1cx 4UsHJrcIGAc8A/D0SV1MweNQNjL1M7APBB3sg4o7oCUEbMdoRMMdlEgMAMXvWDwDxg4PsezD4ppa g8lfmLZHwAyhzIXLM0AYMg+9ahYHGG7NiugNN4Ysc86H8tDzzDrUpyUN0RAwdJqyttD0HkkvDcvT JFJN9B5IEXw1wwxovfXXqyW1M9h9iE322f+uinbaXq/NRwgAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030_image059.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBwEExgYuAEsQx9GUEMZmUmBgYmBhmwLCsQczLBWEyMjFAWI9P////B LD1GCagYN1wdD1MCk4OgEJClxsbPIMXwH6SYQQDIPwBkLQPxBBkY2IDquaFqeBh8E0syQioLUhkY CsB2/2Zi/fcY7IYJIEuZWJgYBIIrc5PycxgYosW5xP88EWK4Mf9z+UMgVlD4Wl4unvaBBahQF6ia A0gbcdUx/gS7V4OgeYdFuRRwm8fIAKI/IJk7nRlkhCYx7pTA506IuYxwc6eyE+1eRVLca8yJ7N6G fwxQc0GiIHNDMnNTixX8UssVgvJzE/OIdG8D42t+kAnucP58XlASyMyC8Rk5wPJwfjUriO8L56cy ocpbMYD4uVkQdyr8J8+d6P5/wPiIDdldDxjdGCF89PDAEn9SZ54KER0em/lARpyD+8eTBcRfjM0e CvzTwBjICzJCIYsTyn/JzQxkJebkMMBEbnKC9KTlFynA9LSC04BCPhc0x3GBcyXYKdB0IcDADubt AedjRiYmpeDK4pLUXIYPILcwAHUoMnRBNADBi+dCDOjhwAyWAQB6AwfgXAQAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh9gAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQAAwDv ABsAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFAAUIDQUFCAgFBQUAAA0ICAAABQAFCwgF CAsFAAsFBQUFAAUFBQsICAUABQUFCwAFBQ0ICwsLCwECAwECAwECAwECAwX/ICCOZGmeoiOg6ECw cCzPpUqL7q3vfO//soLhoEMkFMDkTEi8GZHKqHRKrS2aRcarKnVceQgtd0wuo54+ptmH7qnX8Ljy DW5A5TT6DmFHFQIBD1tURg9NhVh4cUYQZwmAgAoIEYkSQ0lGgJcmfJqJnAmNJ5mQkpQklp8AA41/ hlQODYFEsbOjDZtGm0qkkZOqPrF3I5miAMUlBYJRsa8mErYxwqABxsgkyoMpfavOU4gi4Jy4hwm7 P9fHj8ZKA8skzdrqwwCxKzMS9yeu8gB/AfpguJMXr0SbEfaSBaBXRZw4OQVJHFQiwduxBu9K5IDX gN2thTAmUMiYosLIficq/ybiQ3LERoQdFTIklMDZQzgsUW6EBnJANRF/zoGyCC0giQmf+AiFaXHU Ap/DwlggJ+NmURRIDVKtJwuSMZ4/R/wR4GplV4DEapZrSgpJraUjwAJqCeDqiawpLhDIp7IABHfA iG3l2hQGS1U+4ZooQBatSwU+jZ4Z3CzwLYt/7vARVZZUBQwDBV+CBsWh2hOA43oUPLMGRsskBhgY IKmmBQx16XLc5XO14ZqDMkkOSeCPMcaFUJqIxTssjeTYQIpQ6TJsUFWbgTo2XZgR61FiZPSmISED bqWUlMJmjsVuXEjRwgGH6XjGr1iiEFxRP4P9e6NyWQSdWNJlJ9grY8Xg0/92p6lT2DRA6eYAbvjU Nx18r/DxxR8LvJAQDP6pI10J7qVF13gy2KBeGC8k2N9WmcxUonwkZbYNO9C5iFo1LnKHWEap7Agf JCTFmFJ9LqIYmmGv/TdOdw0uFh9qLyBC23S6XdaeheE0aVCU/khnHInL6EhmiwzaBKY6uTQwnD++ HSnZYXFleNpNo0Q5pmu+8cdCJzP94uBtXSo2FBZ7ctTnYGFCUZmJRJhJ4D09NognH/pAuNwFsBG4 Gn5piQLqRcY4wKmp2lQU3CP0QHVLnM9INuF7zkhaz6l6oZKRkbGNKFFM0d3hHqbaDedqmPf4mExG qeX55pe+rjIihDYi+4X/QEXKotma2zxbVQL6LCmcDkt2OSKe3Wp0rrbTbWIrV0N0IoAGByiLigEb 7BcKiMDGACikLjlDnbQCP7CBOYloWh2GymUT3ZDwBQQWgiv0EkiqBiPMEUMLEtnwrmcV+Agg4UKy FE8PTFVNJ76cta0tH8Ig18UtDJllirgx9iWs+Bhaxqw6S7TvD0Eq8kO5RouHxAT9KNPpn0ckvcrS TRf2XNRSgzF01oZpgQCnoLQWhM9ksPg1dljzoAfXMg/RLNsoeHHArCfIDUZ4RstN93LXZqEc3Oo6 B/iOkIm99w1XSg1V4nVTSK7Yg0e+B977eGvCAJbjRPlimcfWueSgn7EAFKGhA6Ef6aWnnjW6ql9t deuw8xACADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030_image061.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBoMExgYeAEsT5mM4IYzOrMDAxMDDJgWVYg5mSCsZgYGaEsRqb///+D WXqMElAxbrg6HqYElgZDISBLjY2fQYrhP0gxgwCQfwDIWgHEDoYMDBwsQD1QNTwMvoklGSGVBakM DBvAdv9mevSnGmQdwwQQyQSEAsGVuUn5OQz1DkCBb8pct1WYGOt1gVjhAnM9A4MBA9BABl2gag4g bcT1i6mbGaRVgyjzcpW5DmA3jxFMf0AydxoHyAhNYt15B5c7IeYyws09I0CSew8S697roiS59y6x 7hWWJ8m9h4h1r5wKsnsb/kJS6gRw6mMBmhuSmZtarOCXWq4QlJ+bmMdAnHsZmCP1QSa4w/mt2qAk m5kF4zcrofIvgf3nDudrSIP44XB+uxiInwzn24ig6u8WRNXfzQviu8H5bpyo+n+zoer3YkHV78UA 0Q8JF4Z/5IULengvYJaVZUSydwEziwSInwXnu/Gj8oO5UNVPZYTw0eMLR/q6T2x8BYIEGc7B/V8g CeIvhvPncoP42hjhgSP9HSEuPB4wbgGHh24WjJ/Lj8rXYYLwsfiXovTJrA0yQiGLE8pfrQEsihkS c3IYYCLWqiA9aflFCjA968F5RSEfxt+sCOLrwPk5wqh8bTYInwta8nKBS2ew06H5TYCBHczbAy7P GZmYlIIri0tSc0E8LgZFhi6wYhAR8kKIQe0fQz16ODKD9QMAYp7tPmQGAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0030_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhtAEoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMACQCv ARwAhAAAAAAAAAUFCAsLDQgFBQ0ICAUABQgIDQsFAAUICwsIBQAFCw0IBQ0LCwUIDQgFAAAABQUA AAgFCAgIBQAFCAUFCwsFBQsICAUFBQUFAAgICwUICAsLCw0ICwsIDQECAwX/ICCOZGmeZiMMaOui DcG+dG3frjrjfLzzwKDwpBvafMakcslsFgy/ZspwkFp5z+hV1KBuv8EsmNStjs/oNBeqBnS17ea7 PY/T2eq6fc/HIRJ2Cgt9Un+Bg4RjhnGCLgwBkA5fDQ8QZpSWiTQNEZCen5kIn5+AIwwQcCIFnZCW DRKpRxGScZyjoGaitwGlIqepq56usEmctHsKoBOjCcGRALq3vQC/Lc4Bw7E1xiiNtsdNj9hV4pl9 19klydPQFNolCIgmj+Zunewlq/KcqCQI7sh4wQN4I94JembsCXShbwS/H//egeF36cFCewRtGDw4 zuE9hhH2Reg3ImKKCKUe/4GTU6liPRINuYyUaAOhx4sjkq0sUOHGKnzQAsjzuDJfSI8kRSh4qUZn vp4+UZoQNVRmUaMikwJYmhCMAnwPZQY4xiBjjZ8nqJ68OiKmPa1c541Ng6Be3a5tj8rUOkRtCW5k KkUpgNeFU3VCUVig+eIR0DGYBhc2PJdEsqojFi9xrAinR4LJzOmxcdhy4hOak3AuoZKuXaZoLiuO wolggccu7rLGluoCY5CYhTTaFME27twv6fX+DfyLKLYAYhbAkIEkAugtdJNQjsK3ErfURpFMBmno ulWwr4HTDg32GO4nvG+/qAA7EcGBK2Pp1E+cWYw/kMfXC8M1Rp999yVFif9++/EWXgD/1baDgMzB wyBHg8SgAX4MBPdCZPkheEIw/UESYXFRtMbFAwA94s6CAWwgQGmqSLXgMeyxV6OD/sVCnjCF3YjD YadMlsNMMCEpxEb2gKWkhFsdZ0KBlNFSJBBh1TigHyI52Q+UX2FpkYicfSXhaLJohV6F/nR5El8q blXPOr44mJY5dIqQo3tMcvKYn2cpuY1Fn/xHw5qmmXWNnSagVWdRFNmDSJw1UAkDoZ4YeqigySjK SiuxOBoepCMdwMmkF9JwJWljvSHhdWEIuhWEPyy6ZXRSPfomXipSkhGiq50QV3i97FmYqJT6I+Ks noKyg1uWBqqVX7ulut3/nANGWhebOXmYpDzRSrsDtfNZe21CS2lB0bbFtFTpWLDqU8AKsU57WrXY rSqnuqXuRssqGWFCjmco6FLsa4Xpm+6I9NZArinPzNfLbWSgCJK9wQGsjUluPBAcRYDCYHFOu3gS XLAUp4DfiII+XKOm/hBEyccjaZBrDitfam5JEEyAagIEBDkyCoiWdG+SMOsps8dE9Dvfv0MLTCzO vARr7FRLeyjOLbC5jOt/7BGGpayyTUlwxfKIWjEqyfIQLjz1iD12UmUjJuWpeQHFD41LPHcpBBjM II6UR8J1NMnH4V2j3rKO+vIOUgfbqF5WI/yXXrg+VhZjdZvGTpZDSJ0X/1+ioxCnvhW7M6xw3u7F 7V/uaklb7C2c7l5tE7inhN+w00dr6LTjSnrwcpF1+9C6vpWQryxIHhhJlSeko+O+6P6EkZMPzxR4 5SbNM14PQ9nC6uxOPsjqPNX5+/it49q+Ld7rGD7ywr4Ghz7oQ3WT9wV/PvT0D+Jfe8B3OPF1w34s w0yc6hYy531GcBe5mmUQWLD2+aOAyBMS0W5WpakcLVi26IWvOLCCmZlOIBqjxq84KKzWafAFixjf hcgluRA6hEUkHIAJOdIMi20uLYSzwfXatMEg8i0oQwHhR1ZEgRzuUC74yFPHBMK8Ov1pTLgSSgc8 ILrSdayJJWRaCwwIw/8P4iQajJog9pIElEXhxBaisUg/1KZG9R1udd3wFhpvZZUX0DGLpLhcR6Y4 RxbmJBNb8xBgOFIyz6SMCzI44BrzxjJmVGyQCyrkY/BoC08Uy5NGA1XTTHSBTjTxUwno5EUyyYI/ ehAX1vgUJIKINcZwLAipmYfubpkdAToBD7nx5WxMt0thimEPvAzm6wCQS9YUc5l9QJ0mKkbL6AAT C7hJZh8/ZMgxKECAxwTCI2vZtGVtRZhSCNlZromDcQ4EDoucZkHQGQdpwrCaDxQZWzpUA3sqgpYx vAEZK7ZPC/oDn+HQXf/GBrN4bseg8iRoRKfURGJswwt9a6IYp0CTb3KcwKJncOgYMbo7jSqSnUcy pxQ8CtIPkTQJ/+DARv+C0oliTaYQ5YMoFEqEhiWBPLixwCSNxlMpVOMIPjUCUFsgVBwc1Q47HSoZ kjqEpSpGqhO1qk2XMC9oDkqlgaBnV0P6ALB+06t2GCtkyrrVtrr1rSwBK1wpIVe42vWueM1rSKlw Vr2O9AB99atgB0vYwhrBFjm1K2INy9jG3iAEADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

22

All to all traffic – many shapes
of equilibria

1

4

3

2

1

4

3

2

Basic question: how to characterize equilibria

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0018_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXQBWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALBYAEgA3 ADAAgAAAAAAAAAKbRA6py+3fgjrS0AqzhvfaDobiSJbUhqZft2Lq6yDsB9fameD2Hk0eD8z5dMGd y1AsHo/J2rIJfEKNDOY0Jb3CsloVt4v6gm/VsbdsDqPT5IWVvRbCM+K5O27Hv/P1PPLu1wMYOChH OIFH2MeXGLho9zgXCTfJVpl2aZbZNfN32LkniZCDMwo5OsLnYcLa6kqiesJCZPlDFMo5WgAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0018_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYQBWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALBUAAABL AFEAgAAAAAAAAAL/hI+pGO0Lo5xUNnWr3pwF+3XimIRURqYVuprqi7mbDL9sR9djjvP6qrv9gD/h MOJLGY8lpmE5vCRh0GDV6nw+sp6s44plbrmlKfkI1qS5Y9L3HNOuF995rV7f4ff8vv//kNfyBnfQ ByA4aIZmONZWeFf2CKmEoUVJNWGH2aS5yGlJBDpDOqrGsUn52WiqKZIKt8rQiuRGS2d727mjO5vb i1gJHPzbKzuMy4t8fLms7IyDbNgj/RRdTXyKnX2ybS26vcgMajZO7urtC2E+6sPevp6evCsv51gv ifLeSjjetv8qg783k8jgccMH08GAgBo6fIhwj8JEDKUA7AGLzkVjNBtBEBLTcd1HJxlnFIwSMl+h khaaxQrJUkXMabf2zQyiJKWNYzdBqtGJJsnJao96khvJqQAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0018_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhaQBqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABn AGgAgAAAAAAAAAL/hI+py50BnZy02sugxrz7f2gbSJamIUbnylpp0Mby8qrzzcKoiPelvrP5hhhg 0EhMSpAPpbMhVDCfz2mTirVKsVUXVxldfonaTHlsOmfQOPWaHXO/4TmQnE65z/EkPY3/kwZoJzjo 4bdneIH4p8jBuOVYVCjpFVi5eIlZAYnQafgJEApKuJl5ODoYxmn62JGquCrW6npKK+qiJwdrN8Iz m+fw+5s0YqYl+zBlTMMrnKwMFay86yyFKHvGBG0W9xlWJsS9xAsbhex5Agk0vmjEnr6Tg40yY0Os Yh3i3v4RkRKCmbc8Au0BFFVQBrIaQ2oc7PEv3wswDinymFjlYTGH2Al9YLTIcWNFMgwREvMYkuRJ T/qOSezYYmWjNvhkeuvX75EOcTB63pCYa+C+SDmDolpxThpCpKmKNou0Z5RTckevAVv6qiVWTuio snSHcgK0XdfUTO2FxOZXVs3SwkT59gpbKGor0btlyxLeabX2Xs3rd+arwEoPERY8+LBcf4rjlWrc tHE9TYq1BjYnGXNmypU5H5YqWR7j0JMNk8Y1+vS60wH7skYNmLWu14u90h4q9jbUwrpxJ+pd2irw stGGU3tnWZLG5JhKGnd5VrbG58ejk55OnRqcAgA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0018_image066.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC51SPUsDQRCd2cvXXRKTXBXEYrWwEAxoJyL6B0xh8gPuIhdMuPOCCYRok9pCrG3s /Ad2gqnEQjvBYJWIomAjiJWQc3fvg1ywUBeWfW/nDfNmd+5vr05ALE3VCMgc5YrIgXSOAARmRDTK tkx8RBA9hMRxHIEKmPfukoEuRTSiqSpD87EMTIPDxZBlvMfQGduUBWNMn/Q0KdjUWzvlTsMAaIja X6Q7ch0e86IQIZAt1yyjSYtGm27Zlr4L/dOP9pBtSj/bl/mqHWG6RaZOsHNZ6eJTjqcWOrLH9bTE EKXU8BXpNFesUl/RS0wqzISr8PlGHIXCz+hHeYZumoZ/cy1xH1V7L8hpSSLHDnwRzpfsyT7xT30i 8PN9rN8F0a8e1DmYCnMjxfl2wO/kMD+K8y+s1X1eAB6v1F2f1PmfT/B8oudzgCsZHKszwH0lzB/A 9fHDHBBet9SxKrYJ8JZXhjfP6q/fZyTqrgX9rSfD/BFdrnhTqYjJFePnzWQW4oJdiFlHQuZKnWbL sMDmdYFlzMKhm8DW64sKk28gicg3B3oKx4ADAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0018_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBgEjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQACAD/ ABcAhAAAAAAAAAgFAA0LCwUIDQ0IBQAABQgIDQsLDQsFAAUICwsIBQAFCw0ICAUAAAAFCAsLCwAF BQUABQUFBQUFCw0ICwUFCAsICAsFBQgFBQECAwECAwECAwECAwECAwECAwX/IAAMQhAQYqqubOu+ amEaB2y/pIGI+X7/wKBwSCwagQXdEZgIKF4LBkCmXK4ajoASq/WtBo6HjyS2ms/otJAkVa9kpmcL iwIsqukeT4BXgcsjAoBuhIWGQ2Byh1NOLjJ1hnqBfYuVlpc3STWVMopvJ4uSkpikpaQJDxBZNIad LFwmAW0ATSazjApUXiNZcSmifLuBJihcgAuNRchdhctKyJ6IWakOlGdgAdR9YBESCH/CaK4tj78O bbokJhMUd5u8ZU11wNZ2eAmz0ETgtNFm/Ame6FPWqMGEc4T0GUSoAssxVjeWxZqYLEbFT5AS4EGG Lls4MB3l0PsoYBYYSEZA/4rQZEMiRV9+GLJcgiwjKCgvJ/qzc5NWTxF3vAQtNI5FOV63wCgp6mKZ yGB7rNFJMfPIUENXz2DxpDHckq0quvopGXaQGqYW62BJyqcGWhUcx41k4S4FKq9BEh3Sm+buL0F4 jfjdY3bqnltnL6ZdKWuFRreK7bKSC3WSMDJjHOwUcpToTytgqUb+qtlitKxVW+aM5e8tY7XVvOhx PY5ylVE8SoswfCT1D5cvPfleUjXHu6arYVKFOOk4LUB8F4hpIMG5EdeMbCri67om46e3Ky9/l/U6 8wYUUkgP/KMqepr3PAI1qyy+Wb6hWzVu4T33zcGuOfRNFgpU8E1luD0HgeAFB7I1Gg5h7FAAfVbw M+EO6mz2QjmJnLOAdb2B0iEDHyrUCx4ypAIYaL0ox8tE85SgnEQU1mLABVkwgA0xO/akzha67aEF iBvGckuK7LVn5F9DDmEjAlw8gaQZT0bJk4aBoLAAlqZ0aQ+IGCQJBAkoFRJmHgKU6SV1O2BApJdd sjEHl0GwuUgDdAphJ5zqPTEAg3zyeVd5gVBoxJZ7rZgGooGOkIFbiDVKyjKREjLAo5KugWmjWNCw gJqZhopGp2+KmgKpoV4qpqmsturqPxlckN6rtNZqa0ri3arrrq6GAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

23

Uniform All-to-All Traffic

Minimally <= i>B-connected =3D Minimally

(strongly) connected (MSD)

<= ![endif]>
Conc= lusion: Stabilizable if

Circ= le:

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031_image068.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+Vba2wc1RW+M2MbsrAkTSCBAOKWNAik2t6ZfaeUR14igkDAtKQqyF3vju0l+3Bn 1y+5+VEBRUWlCi0qlEaAQn9UVYNA5Ed+8CikQGlJSiVUAnlCSHgUCiSB8piZ7Xfuzs7srL0mgcRG 1MmZOa97zrnn3nPnzK790tZn7mHi50NmsssEtuo6ic1gTPnBmYydwD46gXjtgPPaZrJVbGXXqu8t Xraqiy+56oqrrlm6bDn/LmQS4ELn3hEKhdgR/5wI+FT26BbyJh1PjzQhU/b7k1gr7rJE1gjrkM7A 9SzAZ3KlUtVcR0KpRZbYZXpuSC9n0ykWCK771Ry2/b5Dw68COP9w+J7Tey+u2pSd8bOER8YeFT4l WT63a7RU1vOMkS5jAXYeu41sswp+zvr1HCcmRdzfhx2K6GT5feVFhbCT5FkmY20iP+cxGRnwcMYs gS/EuP9IC1d2Ud5WGXoq35PT+Q+7ir1lfQ0finSEbggGOgcGukupIZ2LS0bv5Z2l/uLwQKpP52Nr iQGdUreh9+hrijwW45lsuiz0XGaP3pctkCVIunuKI90jKg9VTbmsUYflU9O4Fok2KoIZ1ZxA0qmc 3l3u17tJPGjovDeVK+k1OwPd6Vx2wMdbspiP4Z+QjXJ9JN3vmAc94tLO4P5yg8ZwxmOsDQZK5eLA gJ7hhWK5ZpP8lY3BaqLW8ixdqgZrjmkemGydYeKMjONgno06HmctH+d9fC4mjON4V4zkqxj5OFZo 7Qyg3d4ineREcCbYLyq096v8IPGl6m5vkWXZWaRgYIxX17y6E/JF1GqRO4sc4kYuWyBGiDsbwWEE A45KQe+rUxPrXtBRFeV+kW4sz7j1IJ/u2vrvKk9lMv6l9t9dhWCA19Z6ZJxOabCH11dPfcGRLJMd arAxOi4Qnw3Q9YXXaEPI1ox4/uvjcvzmB3PVce7k1ox6zuqDcJzUDUC26z1gYNlIFUq5VFl3fdVM iDtyvJaPhXj1n6Gny7QytCA6nQF6IRMM0LOKdsNrM/fOXPjNVV3tl2aKPXq71hHi2J3LCQkGFi68 NlvO6Yt4Omukc3qHPlAi5hIckuWisYj3Zvu0jD7Ev68bpWyxwMMdGl+VKqf7c/qQnuPhtKsN6VLE u4h3DRb4lcUhrsZ5SF0UiS6KhrkWCmmkuZxsGjdekuk39L72SCzMz7+A+IuLg4VMttC3uDiySEyJ zkMcfyRbmeorZHvxfCEXi7hK1SMiX1bILCnm83qhjJg7v7VcGygtpTMZztzDORjw+M7x7DE682Vj hOdTZSOLzA+WYSVdzLWrlNmSXu4zUqNreU+24GxIEoYgowB4/bVk9PU0Kqp+RbWpolZTVD/HYtiv 2NxihI+pRxRj1K/Y3GKspvh5Mcb9is0tJhrzGI1NrJhsVIwlmyR83NIktCaaYm2iYaGjThalqnk2 KcBJljvsaVKEk2hGPE2KcBLNaKP3ZklSY43em2Yp3ui9aZbEEnmzniROsUberJtramKNvFlPoqk2 em82d01r9N5s7lq40XuzuWtijaJCR510NTWxRjGxl7TopJpijeJCJ5yYVDPu1WXUvU6omfA0qzHQ dULNpKdZjYGuEx4zIU8zkahdJ9RU6zQjzWYUDIinEXXVwUCtdQiJ3tZpRui8d/oLOvZ9BKm5vUex pIvR9V0IOr1oAo80LUFX97EZDKi83XnuUgyd6QE+5lrwzQTP6zG92JvN5XzsPoOP9Rk6uk9D9wtK ENB0fNxSio+NYxpQnchEjo9VJ+Xj5vlYNSN+G2AbE/ALfMxJgT8OhFE2imsaousHG28zfmYuDa5e plDSqYEG2Y2u7MZittAgHHaFw9lMYwTYAEKMO3ZJ0fBPh7p4XLBG/lEUC62Wn5sRljKpkt9HL9as F2RvsVD2D+gVA8bz072O/fGiYZEydB/j51LGJnD3lF9SwDwygwOcID1oGGhDahOmnjHC2zVuFHM5 oeC89VC7F6Z9KQTUAKLbPZ7a1WqkMb7NkGkaep1tMuGj/K5F+9pQ67xzqZEaXpZDfaILHQsGZnSi +FOFPnSs3jvnjM5SOWWUx7NHjVTGxxhpZIz6xX6jqD6nlxN9nTMzh1VVGuHUWnNhV3jDtqPjBydF XUi1kFMG2tsZ7qkBvM4HdlkVA3tt7airdqGLqdHkYw2dJ68KlxXKuqFnusqiuXc+a6i9PDsaGWew T9c5SCg815/njhriVak+9N8qV3H6iQ42n8X4XBY3rA2O55jz0BX3EvXu+M+XZ/t4sedGvESUeC+W tjjsCC6l+cerT58cmDj5xNlbTUY4FE3ySCQe4nkehkkeoZYK7wR0bkeieDYBDyUJDzn8CPRjxE/j xVQvVl9Q8VKhhqPiCBc3NRaLdeD01nBJ0kUsA3yL9rvE+6i+6EIhpgyjONyvpzLCjush3+jZi0hT SSeZbIgINvGIgBd6itW6f45nA54Djmc3Jf48qBoerlocychzVY0RHiOvqhpXuZaEa+D0TqLFk1U8 LPiRcXnQErEJ8qDG4x1JnqALMlE4slR4TvJ+5+OCSqqRhqC+eCpgIIQ1o0xoyTCCjlGakZsI4lcJ TYaiPCkWBVygYbVpFqKxuixUk9Bey8KRJcF1kW9w7IYTT0wQzheffySOatBiESqJSCJMeJgyEElg 72ETRgROWY+FaAUi8ZjgR5uWhC8JVAzttZLwbYSfOp/8fCx/JDfPh+cu7w+jPrw4SkOLJBrDO8Kk OGe/mAIdMpTcqPgf4mGURf3zYWJj/oWdyKao6mNo1KmPY2u0mt8vb7Tz2mxeL7VfU8ynChxtj5qo DkI/U8IjIBlHjxzHJS+2g9P08vMjFzhm+oWdz7ESSUZDE5rRjsqMlsTrkJh4g5nw0Zuh15MGK6rf Su1ZGQwY2HqznE/6T2NzmPjwUjxanWdmMOD7huBIP6utfS1C7zU1OLLvb2TfZ7ctgr9Qkdndynz7 LmWFXaMJv0MZcmnCb1E2uDThQ8rzLk14Sjnk0oSvUOZVajTh7UrSpQkPKqtdmvC3ZcOlCX9a/rlL E75JvsOlCV8vr3dpwg35jy5N+Gr5IZcmfJm8yaUJnytvdmmB19GEV6TNlan+Rq3V+TapZYq/WWsR n9a3iW/WZgISrfRd2wJkjbKwQH6icqZM94cqU71H25yMtLJTxNp8NaKqrVObW0EJNsdOsLm2R3M7 yRa7NOEXsQGXJvwSNuLShK9gv3Npwlezp12a8BvYCy5N+Br2rksTfhOb7e5gwu9lEZcm/HHW5dKE 72UFlya8VfqZSxPeLv3Wq1jgq6U/eBUF/GbpEZcm/BHJqyDCt9TRhP9rGirK2z9TW1FeJU9UWRez Jdgt59iquH/HJnrqT//aHq5V1lchqjY3b14lWVaSbbO8StpmXcTut7xKut9awQYtr3IGrdXscsur nMutNWyB5VXKAusmZptepdjmvWyn6VXKTvNx9pjpVcpj5l62wfQqZYPZKt1mepVym3mu9BOXJrxd Gja9yhk2V0v9plc5/eao9COXJvxm6QbTq6QbzEek1aZXSavNLXU04f8ETHUleftlaivJq+CJKmmj 1C2ysVG62twk7t3mdD0NWtxK+ipE1eLmzevyPrDuUp61vC7vWesO5R7L6/LusdYpv3Fpwm9RCpbX 9RWsIWWp5XV9S60fKxe6NOEp5WzL6wLPtlYon5heF/iJ2a685FUG8KCy2fS6wM3m2/K9ptcF3ms+ Ld9qel3greZ6uWx6XV/ZNORe0+v6es1l8vWm1+Vdb86VvcoReB1N+KfTUEnT1+XVKniiSlqnbLVo h9wn7i9aRE9/t/dlojrW6zVdJ199D9HprNdp7DB27iHpevMgzpb3pB7zHSltvillzNdxfxX0bvB3 Qb4Teruka0FfDf6VkK+E3hXQX4lxV2L81bBzrXn4KCrh2J9RHWK9p3dWX8f6rt8vmyuHpEcrB6Un Ku9JT1XekbZU3pT+Unkd91dB7wZ/F+Q7obdL2gT6YfAfhHwj9P4E/Y0Y9yDGPww7myqHj6KbP/bn g7dfpm9WX+/zZSk70V7CTrYXs5l4E5htXyjecE+1I7iroDvAb4f829BrZy2gJfBtK4J+PcFM60Lc Lwa9GPwlkC8VetN9vkznrL7e58vvlRPtB5ST7Q3KTPs+Zba9Xplj362cat+J+x2gfwn+7ZD/Anq3 Ky2gJfBt607FwpPdtNbjfh/oDeA/ADnZm/7z5XjMqslvrM8SHz+D2Hx64OyPm/7GemvDb563TsHn xl/2vDp6z0dyXpH4PLH/ZHYyZHPZLHsuani2gPn2KQJm24qAWfZM1O5sAaQ3CzICyW518KnOY8sU rOBkn0211eXxOqeOL2AvKKfZ25T59mMCzrCfBP208g37WeUU+29KANAGaLGfU2TwGGTM3gJ4Ejv8 CUWxH1daMa4Vd8n+s1KxtqACngE8B3ge9Fbwt2H8NtjZqsyw/47q+asyC3bm2E/B15PKPNieB/48 +3nAVmUudAlOs/8BoPimeqXajvrEPTYr1dLw2QeJb3VW6lK2XXqr8op0oLJDeh29zb7KXsA+wH5p f+WA9EblDcgPSP8G/S747+H+PngH0fccBnwE/FPILcgqGMvYK4CXAdtBb5dsB6zKyw68AtjhwE7I dgF2A/aI8ZXKa8D3Qfa69Bl8fQL4L/CPAB+CfxjyQ+i9DkL/IMbW4APY+ADj34f8PehRrO8A3ga8 Cd4bGHMAY/bDJ831DcTyVmW7A//PZ9/Fzk44m+2Q5puvSfPMfQI6ASpAA4TxZhQ29wMOSBEBOxzY Bd5uB/ZAdw/G7MHYPdI5gLMAZwLmQ16FXYCdgB0O1P7+o7ZDa39xUstP/d87KWIm/wNmauLKyDYA AD== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhiwCPAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgCK AI0AgAAAAAAAAAL/hI+py+0PQoC02ouzhnL7D4ZiNI3miYpdyrZus77yTNf2jee6We4+LYkFe78i aogckpDGJiVZCiKUC6izSbVIK9mrLXbbel/gnXg8OmOJ6E15/G5z5Qo2/WG/x+/TPJ/0Vxfo4CdX OGhweLWH2EfH2CiIphgpuViZQfmFqaE548lpaRbqAZpiSiq6mfqBGuLKmgDbGgsy21n7CpSrInPL K0sG3NvyOzxVfJx2qrx8YtyMzBPtTExtbXs9na1dXdq97QYejjuOnWnufQGdnijerlsOTys//47B Pu+aD79vH7/uH8A5AulpKWiQIMJ6HBZ+O+iQIZ6IEglRxDfBE79+/2pgXMSo8eM6UBv1QRSpsE4P SCgdSdvSpWUVMVJgxpTZR8iSFTdxHujCc2XJdmBsSvPp8eeeoURPIq3ChaVMklJbUmU6zhTWrAGf QnXq9Se+sMG6knVn9iyqrd3WnhWbNqy/t7DYUqtLtyLOWXab3ep77K/chD6NAeZl+Cm7w7EWFyYn kh/jUCUnYxpquRHTzIO2cubD9rMeXw4Bi4azyt7k01hysC7C+fWo2Vx/yE5tu+2lu6j9tqla6TYD 4IGI52Yl/Emq5FEvM48L+nkm6bKou6FuXHN2Mtafsd6+PHNHcD1hEC/PkcnMoh2sFE6yc+f4t4nO zKcPF7/+/fwjgQxXe19/SnU3zH9GFAAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031_image070.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBYIJ/AxMAJYl10ZgQxmGczMzAwMciAZVmBmJMJxmJiZISyGJn+//8P ZukxSkDFuOHqeJgSmBbICwFZamz8DFIM/0GKGQSA/ANA1nYgTpBnYBAHqueGquFh8E0syQipLEhl YEgA2/2bifXfY7AbJoAsZWJhYhAIrsxNys9hYJgowXVrxhMhhhvzP5c/BGIFha/lbpJpt1iACnWB qjmAtBHXPEZBJpBWjUpC5mVLcvXgNo+RAUR/QDJXnR1khGYlEe68jc+dEHMZ4ebu4Cbavb2kuPec ANHuvUOKe3NFiXZvHynubZZCdm/DPwaouSBRkLkhmbmpxQp+qeUKQfm5iXlEuncB43s5kAmZlTC+ oQQqv1YclX8T7D93ON9GGMQPh/ONBEH8ZDi/hg9V/wleVL4KD6p5CzlBfDc4v5sd1byrLKj6FdH4 tUyo5rkxQMyDhJvCf/LCDT0+GJhyRZDtZWDK4ULlCzJC+OjxxUBhfC0Ex5dCJSeUbykLLJoYEnNy UmEimtIgPWn5RQrwMAOnHYV8OF8SxDeE8x+Lo8r/FAPxdeB8BQFU9Xp8qOpdeFHVV7Khqm9nQVU/ lxmiHj1OGCiME31uiL1Ywhw9T9/PeCpEdJg/BecJbbj7TYRA/MVwvgE/qnw1Byq/kxXCx+Jf9DJh Im53ofv3C8NRcBrUzYfxj3Ah8xmY9nAhu+MLQyYjRJ4LWsNwgWshcLBD6xcBBnYwbw+43mJkYlIK riwuSc1luAVyBwNQhyJDF0QDELQ8F2JADzNmsAwA8mXjZUwHAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhwgEjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABQC7 ARkAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFAAUIDQUFCAgFBQUAAA0ICAAABQAFCwgF CAsFAAAFBQUFCwsFBQUABQUFBQgICwsLCwUICA0ICwsICAECAwECAwECAwX/ICCOZGmeoyOgbOu+ 8DgQcW3fpYrvPDv3wKBIJyzWfsak0lYwHJbQEyKhiFpFzefVOq1uo9kvtCsuBx0LrVmJYNDW5zSc 7Z7H1XZg+53vl8h+QmGBMYCEPYOHL4aKN4mNcI+QNQgNXpMnkpiLlpsomp4olZcmBQEBD3xJUw9a rHgtU6eztKkuUxCiCbQKCBGwJpVOwQ3DOxIBKyUSxkuytLWqtwm5Uruzvb+3xcDCwDHIyiTM30HI sxMNtBCV2IvUury+5SPef9w94cvNJAO5pq2UOFAXcCCqb/ZImKo2gtyzWQwHkhIhi2FFTvwo4nM0 S9yIArasLNx34OEphiQk/wbbZZElxm4bmXQsFXLJQGOmjCU0GSBipz8uKQaNFVNjxhimTnkEAFIa AJUABgRkk2DqKylFowaY6IDCC6nSBtYUOnGOqaVPG6BNMmBrDq9HxqaVy8jOWRMD19qQgHYgQ31Y ULoAm6MBXSqB7qZUW8rtlasAIIObqsOBUxMSpmqUKwKJlQF6sSTD20Dw19DLKK+wvFdzZMOXPUcB 3ULxYtOF1JVlOpp3bwRyJuOpxDnqZSO0a/dOUbrx7lVVXUWn1Lzz85WuAZuoQC/ytYnPrif/tLze xrYHfaA2z3DAdRaSAWgvwT3Wd6CnxKO2bd4YetekAaiQW2205YUE7wGVXf95JNQH3331QHjCeOQt lVBa6zQE0YACADScOkpFaNV0JIRXgileOGBBdyXGJBaLgwkYlYyd7cfga63Yw5d6MKA4xIo4XPgi EFJ9UySPLPC3WUn47DhhAEeVYGBUAkxZAG7wuWgYjC0cKSWNVLqgJHGw+KhRNR4+cwEFhBn1BDJe QBafDACeM0uUJ9ykRltYFgLPSn2GmeSNrGBQXVNIumDnKXi2oKcMPenxJ1CBUtgYWoUeetiNKGRG ABoHeIoAkDU82lmkPeACaJfrjVmVNGbKpxmfoh1VCZq/kTind4JN4V+ghTUzn3y1dAdVYe9ZeiKh VTEAppTreffrDqYSu9T/os8eu1iyNmLabLbqRCtCZhnUkVmoCZImLIPYGvvTtqyKySArsDp2a4sB KWkCesrISSK8t6Ug7hAbybLbsBMW1yak0PCyrLcPMOZDww6TFtHAwUrn2DKcfhmbXOhRvLFoEEv8 FaoPPkAbK/7gYKrBJyC8L2cLnyryyCQrWG+K1Qlli76QQqCYvwLWrNUlrOWmGcJkTmNrAo0KWuFK +R0R7ZRDHLfN0oRu6XQ3UHenLIdU4ywvjVNMAGTapNrQ9LhdPystLL6K3eq8/4rmxUjj/Nyxp7z1 q2vec5dIOCX/8h3wNmtVst7YH3U9QXEoQC4il9NopjhzwL7WuMmVd0vM/+RaZ2l2O3HqtoNkmxPc uePEPH63hVmZOaTPTwCt2NCDAwj74jwALhTOWNdWHKLxDoppA6SnAFfoLvjFQ8sN1QRzP2bTdBny iWYieU1d7bWU9K7nY/0uExWfJGfcQ68c7abFqt3vQGPN+4gAtm+tD1HXjPrlEWKXATIQnIYMsID7 spFpBqIBfIBCBuuRWWeiRCs6qeJ/uAvgtQ4IC2YQkB6W480CG9DAYTywVG1TUTkG0L+xYNA7mpHF Bj84Dg52z3uCycu+NoZBcuRMXUxKxgZK0rsO2jApp5AbC7Rls1m4kCBqkIXvdvEsyBlkJh9JBRI7 ZzkkpicW2pABSpiolf9otOiL3kHj8KqolyuGKIsE2CJ5braUAnjEjkAgY8iSeEEoBtA1UrTbEkH0 RqY8sWIPEUfIjnKOB3BAHewgZC8k+UfM8SZqquKBgwjhw0hA6Qnz6AdKMrmDTQaik33ISXdIiQNT 9gGVoQgSYsSkxDxhbAt1KQMgQinGE9USL7d8zCz9kEuaWDIlwYxCMWMZAxW+I11AidoaTngFFWXg Gnd6AvUiBE3DSdMM1CyDM6fRzQh9UwzhZOYNl4hAdf6hDnYYDy87s8B2urMe8AxECFNiz3vu4Z43 +GcznwdQGZSTDnyYZ1RwE76C9uOgXMjnCxrq0KhAFKBiKd2JknmIfVYXEzYUCaNvcIPHinpUnCBF Ckf1udJDhAAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031_image072.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBwYD/AyMgJYk2IYGQAMphlGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMBxgd2IWALDU2fgYphv8gxQwCQP4BIOsYiMfOwNAGNIwbqoaHwTexJCOksiCV gcEAbPdvpoZ/EBdOAFnKwMLEIBCSmZtarOCXWq4QlJ+bmMdwY/7n8odArKDwtbxXIi2QBahOF6ia A0gbcSUw7mMDadWD8/+xgviGcL4N2D/62OxjAtkXXJmblJ/DwFAuzuV85qkQDvsYGUD0ByR7RcD2 6ML5z5hA/M0Y9jCS6C+IPYxwc4VYQCbkwflPwCYmw/lWDCB+IgMXNJS5wDEBDk6oWwRAEQEEe8Bx x8jEpBRcWVySmssQCLKXAahDkaELrAFEvHguxIDuZ2awfgCisyK3UAIAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0031_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZwAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABgBh AA8AhAAAAAAAAAUABQsLDQ0IBQAFCwsFAA0LCwUICwUIDQAFCA0ICAUAAAAABQsLCwsIBQUFBQsI CwgFAAgIDQsFBQUFCAgFBQUFCwECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZEkewmCubOu+ cCyTRDHfOG4ESN4aCZ9wOCIEjj3iCKW6ERRNpdCYlNZ8C0YjKnXyYAdGQOHQckVA1uO4ZYUDQdc6 YAOs2z7qa91bQBh1JykmYVAABlUsO4EmEQcSCI8IWXE5ei1rlTuVRYwiYXUEDRMxd2ciohMUpEac XoklWYkGeCRpJQ+1M3OuaAoPcbSkeV+Khp8Sx0sVZ2GwMIstjxBJhVFzR9nZsJcmsjTFJA/PrTJv vbEMx92W4SWpSxKjJQcWwzTzL1m6mPl2/u2eicgVZYcyEQuYmYCH8MLCgy4eHZN4agY7cEGcAXpw z45AawCeVLzhbISsVVPoHuD6siPAlizu6nUEd8RTEW043YX0ZwQOFjHbRvAJAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

24

Concentrated Traffic

•Node 3 takes prefere= nce in
routing
•Disconnec= ting 13:

•

Conc= lusion: Stabilizable if

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032_image074.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+1da5BcxXW+PdIKtGaRyipTMSauxkIqCGjnPbOrAGHR7lrSSqyQVuKhyNLdmTs7 I92ZO7ozsw8Wle38Scwvy4RKggm4TAWniM0jUVJJxCvBlsAyYDAIYwKWeecFVAAhxMzcfKfve2ZW SOixa2RJ39zu06fPOX369OnuO1Ol55/Yc6sk/vxIekpaLkp/eA2T5krSrO0RSTpDOngG0ZYAi+fM k9ZIq9etWX9l35p1fNngqsG1vX39/DK0MeBS69kZCoWko/5zJnA44NZnkzZ2MjXSgKoBvz4mteEZ YCSNSp3si/g8D/g4YBgm57epkc0OMGm5oo4q5VxKltr/4tvfWSD98o73xn4DcP7B2Ou/lxk2ZQas /vOFRkl6QOhkgcBX1k2UykpekohXktqlxdJNJFsy8Oe8mxdYNs0Sz3chhyw6K3DprF0BKn0u8OOq JM0R/lksBeABtyxJNVFehH5vs0Wr15Hf1uiKnB9WFb5xnZYpK9v4aKwztKmjPVgsbi7JowoXH2kl w4OlrDZWlEcUPrmDCOApbdaVYWWbxhMJns6lyoLPIQ4rI7kCSULL5mFtfPN4mIdMUQ5pwiL52CI8 nIw2MkZ4JJS0DEnJqrK5nFU2U3NFV3hGVkuKLae4OaXmij7asiv5JP6KtgmujKeylnjUx5261Tlb buAYS7uEHR3tpbJWLCppXtDKtkzSV9YrpqN28Bx9mAJtxTQODNYjmCjjTRSMs5HHpezgTdqbfdHS jpO9YphvxQRO4gq1cwBF+2z2OcuCL4G8S8S+Se8gOjOjfXYgELAmqaN9kptzbkZCXsNa1bg1ySGu q7kCEULcCgSL0NFusRSUEQ+bmPeCglVRzgp3Y3qa5oN0OnPrf4a5nE77p9r/dBg62rk91+NNPKXK MPeuHu+Co7Z0brRBxkSTIT4ZqHsXXqMM0bZt3NXvtcvSm6+oZj9ncNsmXGVeIywlng7wtlcDOpZ1 uVBS5bLi6LJFiCd8vINPhrj5V1dSZZoZmhCFcoBSSHe0015F0fDKvAPzFp2/Zt2SnrQ2rCyJdIY4 orOfCh3tixYN5cqqspQXIp1KsUSEZUiQZU1fyjO5kUhaGeUbFL2U0wo82hnha+RyKqsqo4rKo2mH G629sHUpH8JK7FVSPBzikejSWNfSeBJZLBQhzn6SqW+9Atl+VMnLejlX6Mznyp1KusIvXCvnlVKW r9Sysp675JJLLqIeV2qVQjpXGLlSG18qBkpZEkmR2lbLI4VcBrsOKV/Kw7SmxHj6CullWj6vFMoY TfCC/kix1EuZGmY4Kbuj3aVbSdslBPNlfZzn5bKew3xUypCS0tQlYfJ3SSmP6PLEDj6cK1hhSo0h tJEB3PtZ0keGGxnDfsbwlIwRmzH8CRKjfsapJcb4ZPiobIz7GaeWmLAZP8nGpJ9xaoldjX6MJ1oz djcyJrqncHjT1HRFpuAUcxOPCp7wkawMR1yZZOARpjvqcpKFR+CMuZxk4RE4443ap3JSONGofUov JRu1T+klMUXuqI9gp5gjd9RTc0bEHLmjPgJnuFH7VGOPRBq1TzX2SLRR+1Rjj4g5igue8BFnMyLm KCFiKRI/IqeYo6TgiXYdkTPprsu489mSs8vlNG2gz5ac3S6naQN9tkwzIZezq8v+bMkZ9nDGphpR R7vYo+is3dFuHyhC4sRrHVEo31unDkr7vgqxOScSraSI3t6zCc5/3bHOOI8k4vh0NtOO9jBfYu3G ZEMwVeSTjgTfSLCLTypaJqeqPvKIzidHdAVnUl3xN5TQQMPxUUsyn2wi6mBtJULlk+agfNQ8nzQ9 4pcBst6CXuCTlgv8dsCMsq5ta7AuCzLuOH6imgJVKZMpKbnY0LbVaduq5QoNjWNO41gu3WgBAkA0 44ko0XT/cOhsjw/Mkb8X2UKz5aemhaS0XPLryGDOMqhmtELZ3yEjOjTTUxlLfnPTmHAZTh/NYykj CJyY8rcUMI50pcgJqYqu4xhiD5hOkjG+JMJ1TVUFg3UXokNglOJSNNCxEGfgk8ltrkbq4wuG9JSm e2STCF/Nr1ocahuzgq4ohZQ4e2HrdK7NwbVKXyGlpXG95i6HfYdGDFFbSS6kC3Q29FwS0UTTRWQP dVguKU1kCLLppnQvkx0qPqncx5+Xx1WlMILs4h4dfQyTlir4LNi/ohf5ByRRE2ND+HBlO12IHDZL nqzjHMlTWnGC25qj3JomHDrp2m11at1sH/VxDeBFrSjgIWY0XVZVkVpF52A/Pq+iUXu9R5KaHC2r mpwmeciW2ErCPBLHduaY4Q5sRLHeGwQ7cTcnJ5qWZSjWm8Ra447wHN2sppLXMEhdKeJ64Qyj4BkA TQYyjSjS4LGfOO8gciVkxhTf2NHetTAE64P5XKFS4l0L6RKAHE5veKgS5kE5VSmblQgPpnJ6qpLP qMq4oER5sJxT0wqJiYRiECOndFyEqAahw7piyUnwYBrJK5XCmhGEJAg5BUk+VxKdcZ4MUi6hRhw0 gykljZ1FFlXozVYKI7JeyatyRfTHuTGojWgFZZuoQXNKhmIhCocTUqYqpVKOWrEzBzVhBnbe4GCf YMK+GywV5ZSgx0DHPKlyPq2NCetjNFbL1hh04UpGN/wRsy+pE+s/NSEYMNQJxeyXoFFjGykMy7og YKAl3D5zplfioYZxx2msiHE9N5IV2uLQrOnpjIIZwewJEgwYqcAdSp6GlTH5YISqjeB+pyK2TFmw IztRzJqmxGGKjlxBpitpQUl6JyhBpijYqoWOBOwoqpWSiAMhLQFDymNaqVJU9JwmBpOg+c6ih48Y 88RIgkKpIkpQX5R1GbFUzJoCoV50S5NnbaOSId9kJ2EHptWrIGl6JC+XUhXaOoWwpNcnjvOSMdF7 ewWXZ8XsHBeUrPeuL6sZU0bCGo7FL+I/CSu3V3D4wIxZ0RClNdFjL4ooLYoeMWKSEqVl0eNbF1Fa Fz1iYYgajOqxJ10QYFOPbkVTlNZGT5+gQ/Uy1xdRWhN9jlpaFX2uWloVfX61tCj6vIpoXaxwBUDt Co8A6F3RIAAGrPAKoKXUh5xERai/yhkTbg/BQSFZyMIVIThoB0EU14DgoF8yzvvBQbc3VA/69FBk VtRyrqhOCIG0ZgdxeigJ3bRu1zvjiEL3ekdZFKrXu8rM3jBgvVd+FOqvc7tA/VBW08XcRqF6RNHz SMPDqmCm1CC7Y6PkIDt9KTHI/rFRfpCdsVFykL26KTvIzmxTgpBNRihOeWabUoPiDJLyguJOFmUF xa+WsoLiVUQZIecKgNqcRwD05hoEwICcVwBlBMWcbUoHBWdMlAo01yOUBjTHI7T+Nb9kygKa2xuq NZ8ekfxHc+a+EaUMoDlzTQmg4oyC1n7FUUWLvtIw17TkK17ptOIn3C5ijVtzTWt7wubdZG2FQzls vkvWaogA7q0swR7JrX3SPojhKBfs1eWxPhVXKRwjJjva5waxr8qFEdV7ppqLDQMppZk8octpH2G8 kTDhb/YLlem9oHjtJl7BWYdQi2QyjXN6N8qFXKENNwTxZpB7TbJNlvUU+jgXPJQ9OnAhMEsg77Bv peYLwyvpEMonG14ScrOxz8zu68ri7az1ZZF98rA40lZnH6915yPzHH2uOpy2xPvFfE5sxnhgOnB5 TlivRMSzhPEswj/enxvh2vBWbL0lnLdUVRsTDUnzpYBKNW5NI05PPCreuyWwCMPiX4jTcvDONe6v 4kVmiY/oZFiL7jGkuePo3pX8lN3DXSHRI8Tj4l/L7vSawX49y3EUxUX9k20SHydaaCxyYoUKeSdl +DgmngSh4ZMgNHwifLpGUyfMExbfmAhtgqQSLs7gE6+OzAQR6cbWhENPiOd5pBsBH+lGglc5Tlrd oMe6qdyNowzMEuVkV4LjKBNBOYUbk6KZ37oVzHjHzhbneSgUssRQVJ9lwji+0TZmEd0LtbGsIqdJ his936DVY02ym8qJSIM1EJsqTuEbS7/fKY2OgMGxCM4fpBpOiYWTzoBjoe6k7YhYuDtsmxQLx0NT OCKR9DhChHQLR7RwgC0136DNYwU5IBaOJhusOE4HQAoiIdENsyGRZi8RI9XRbvJ9EqdAFXSak0RX TNDJ98lksskBOPlaQyYHWLJAOhoHuFLzDdpcK6LdFAFJ4QCvFcftADI0Hu8SqskZ8ZA70Fgk4jgg Hk44JsXEwFo4QAS/6wBaGEfnAFtqvkGba4XpgFgi0mDFcTognMTZDedOCr5wV9Qqq1aZjqCqtTfF Q6Is+E164xIQXJQLzLLIZ6q9HMJHuxxcDXm/5iaLol2NFh2nM5BhYHY4Sc4wy/TmAf6m9wN2OdTt DMakE3+jM8z9zHSGKDvOEHFy1M5wNeRbaLatC7e06Hgjo4uWA91ZMQ/dYfKxCMRwN1TgXmpGSVcX dHZFzDLl5Uh3i8jAco5GzQwfRnKPiOwtIgP3PLPmd8arAfOu/0Dbv7a1jhJHW95vhdc6YXU4EWuw 7rgdgxyJO6G5ZDAnWIkJoQ4ZSThMtYYci5omIYPBvNgUu4YpSZxTxIezZMza0SwZR0O+QbPHou4o lUUy9Vp0IpZMJOQumUjYXTJ2mQJXHJlseugTlky02z5kOUvG6n+US8axqFFz2F0yLSw6Ic6IepwR 8zgj5nFGzKM6+knOiHdH3MgwnRE7JmdEPc7wao55nNFs0VE5o+m6nclQdhY9UhlewgUwHKcopy9d 88Jh1teT/MLwRZaYrDD+KESZB6uYed70ioocs6gYva1pZVXs01mF5NhkVfSYRZmzG2oWVVgS/nTC wuFmYfFPaVe0hV1+UfargY52HcEx3/pl6hekBZL4sZ14k2C9Iuhof8D7i9Ypfnk7X9iGyvc/337w 0JS/vJ3d8Ava2Uf9W0X7Z8H0Db6No/v9csD328XZ0jl4Lpo1V7qWZWrXsmxtAzAkkAHSqKdBJ2Rq p9q6NscvrpUhWBKBVRFYRwgBnah3gk4I1U69D00r2zxW3gZLbodVt8M6wm3ArajfCjrhttqp/qV6 2zHH2In5xfps8SvYOeIX60Ggq41hZV0pLTV6pMuNK6Qe4zKp11gq9RkJqd+I4BlE/RLQL0b7H4Dv YimBehT0ENqD4OsEfxD9QugfhZyEQfJO9bzPcea9U8z79I7qRMfJnFMcJ3Oc+GwVL8Ps7rrM7qlv YffXN7Fd9evZP9Y3sH+qr8VzEPVVoA+gfSX4BthdqN8J+vfQfgf4bgf/Hej3PfS/E3LuqpO86csT drxM56h++/OKHaet4+WnhsyeNLawp41N7FnjevacsYHtN9biOYj6KtAH0L4SfANsD+qPgv4I2h8G 30Pgfxj9HkH/RyFnj0Hypj+/TOeoPtv55U8CS41vBi43vhHoMXYEeo0bAn3GaKDf0PHUUFdB34b2 reDbFkigHgU9hPYg+DrBH0S/EPpHISdhkLzpzy/TOarPen45Fxn3y8i85yMDX4BMvAgZeTEy8yJk 6AuQqc9Hxv4yMve5eJ6D+gLQ56N9HvjOBv889JuP/gsg55w6yZsJ+WX6RvVZP788U5PZ/toW9kJt E/uP2vXsJdwGXq6txXMQ9VWgD6B9JfiQwVHfB/pjaN8Lvj3g34t+j6H/Psh5skbyZsL5ZfpG9VnP L4erMqtXtzAGD82Gp9rgsTnwXBs8OBueZPBovboSfAPsYHUVe686yN6trmXvVDewt6vX47kJ9S2g y2gneTMhv/z2j8rNL2eKUQWk5dKFxnrpK4ZdH5a+ZGjSF5z6jdLZxp9JZzr1WyRmfF/6uG7X75Xe rz8gve3UH5fequ+XfuPUX5VerL8jPevUq9KT9blsr1M/h/1bfSHb7dRDuDlchlvDqV5J7nyf2pXU 1iLzzrNWUpu0kP17/Qr2w/p5uFctZv9Sp/p0Zc450tlijmaGVe6O5UbyKuMK9tgpP+PNnuY9u61l 5JyHGxN5YyG731jMdhtUn743oHbkzASr3JOAHTlZ3CS3BK46rW8HbuQsC6SFNy4NXGv0BzYaVJ++ 3deOnJlgVfPumWV317cEFhu/260oci4NnGeQN5YF5mGOvmhQffp3q5lgVfNulZAWGgnpcNWtH65e 5qlT+W88dSr3HsOJ8bO9uwUlo04evEw85xhUn/7dbSZY1by7jQYuNEYDwZpbD9ZGA8xTZ6i7kUbl /DRE2szcDXfitkbe2Inb3U3i+V51+nfDmWBV8244IP1v/RvSM05kUflbnjqVH/TUqdw/DW9NZubu OSA9Xh/ATfo66Wf1NdLTdapP/+45E6xq3j1XSp839kjnOm8NqPyEp07lucytU7l3Gt7nzszdcwjz SR7cIn1Qv0Y6VKf69O+eM8Gq1rtnInDYyVlUDgVecOpU7gy4OY3K+dP8TbB399wnvLGTvYB9ip77 ajNh95x+q5p3T4q091jcyVlUfoud79Sp/Jonp1E5Pw05bWbunjvZAuGNnfDSTeK5YAbsntNj1VTf 7Z08zUfKDPYeRM1/ZM3X74PWa5wl9RgdAtcBG4E/BjYZZwPzgPnS1wTaLJwB2pkW5oJ3LvrMRd+5 0gqgH+gDetFu4gxgDtBm4VR7/ti/zT0xnm/8Npear7E8f5F0LfvY2ACFfQKGsQL11exDY5C9b6xl 7wL/A/yXcTV7C7Q30PaGMQCsYG8aX2X/afSz/zb6gH7Ul7PX0faqcRVwNTCE+nrQN6D/BshZz94x 1rH/M9awg5DzkbESulawGnhroNfAXwNPFbyEj41rALLvVM/U7GPOaSdmptoadk9qXixmKiCdhbZ7 AkPGPYENxt0CXzPuEthgfFdgyPhBoAd0AvENoY3QZ/y1VT6dc82fWhHfI/Wzx+vL2Z76Cvbj+gB7 tH4VcDWwjv2kPsT21tejfYjtQ/0J0J/C8+egPVPfwJ4F9qP8K7S/hLZfo+8ByDgAeQfqXwX6Qetn L1t4CTQTy4EVFlaibQBYBawWMn5dX4Py1Whby16EvheA51HeDzwH+rNo/0V9EDasBgYcPA0ZT6P/ z9H+FPjI3p8BPwUeA20v+uxBn59AJ413L2x5vE7jP51z3zetSLhc0th9te3snlqJ/ahWYT+sjQHj KE+AdgPabmD3A/8A7K5NsgeBh4CHBW4EdrBHBMoeVEAfBcYEHgIeBHYDu4C/R9t94LkXvPdC9301 DTQN7Rr4NPBr6Fe0sB3yCFkLOWAr6NsEHgR2A7uA+4H7gHsFtlrIWchiPAWMTRO4r3Y651P3jPh1 eO7r7J9x5idQeVftd6cxOo3tZHfV/pLdWfsrgd3Ag8BDwMO1W4HvArchFgk7LdwM2p9buAW8t6DP Leh7C/s74G+BHwB3od3EzcB3gJ0WTueMtNHy/MXSDWxfdYI9VS0CBfaLqs6erVbYc9Ux9jzov6re wF4GDqD8SnWcvQb662h/o1pmb1a3s7eqGpAHtgm8Wd2Ktq3g2SbwWlW1kBd4HTpeh6430JdkvFEd FTJfAQ4AL6H+IugvoP2XkP08ZOwH/74q2Xk6ZxHvHnIIOfog9pAPkNffR45/H3vIB9hDDmLfOAR8 BHwMzKpPsjZgDnCGwI3ADnamQNmDCuijwJjAHKANmAVUIf8w9pBD0PUh9pAPofsQcvphYFZdA58G fg39iha2Qx4hayEHbAV9m0AbMAuoYt/4CDgEfCiw1ULOQhbjKWBsmsChmv3/BdjRbP8PBfYcef9/ jFnCm/8PTxIJpfhkAAB= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhgQCaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgB/ AJgAgAAAAAAAAAL/hI+py+0PgoS02otzllP7D4YYJ5bmGZLoyrZK58YyyAXzjVtwzvd1DwTWbIhf UDNMKpfM5jDydEqnVORx8UyofNbra+s9EEfhMmV8QZvX2i77LXbD3+pKfV6+Q/T4K9/x1yckZ7ZT SCjoFciwmIjT+OJ4uCGZh1jJRYnpd7n52Ok5A9kWOqjJZmh5WpozWsSaSQbbCjq74hpne4NrwKu7 qvMrWiss4utbbEcshOxyHJoq87wJtrvsBxYdM42nBBWbJuit7Xx9ZNTbbE7abVQ9DByGPilbOA9F vn1NxT8e1Q8wX656gHbdw3drz75H78o94NZAnaNFEBkli/RwmcSJ/xnjYQzS8ESgiljOhTQxkthG DwdRpPT4yqTAFB0JlpQ5k0ZBmAMN5hS50+ZHUfdaGgsaLqKOgD+S4GM66g/JmApTzMtyJphSnhGU WW34s6vWm0KpIqUzdmhatRa7rTX7Fi5Zt1nblu1VV5xXtnn5stPbV25gwX8B1yy812/PRI30TMV7 lnFVxZEhb8XUeG5csZcxTyZ8GDRnap8XJxa90lRn04MtU+a42nVcqbNeio49GjG0yFP5pOYUu7dd W75fD2edGxbt28eTyya+mqTjZMWZa3b+e81062zvZNeuWbrxEkYTzq3o3WdYmkPRj/8wwRu8v+51 G1ORZT0iNPWR0/+4ms13cvFHiBoCnoSFgM+N0Z9z/yUnkH6DMSiHgSjtMZOEoVF4yhapUYRgEdkR +FxeHvqwnobhlTgZDBLxIqGK9LFYk4s6pRFiRC/GxE0HyPwoYzo3itWjfzpq92MuRabYh4YUogdJ kAbVYwNE5bHCZFdWRohlVFpu4KJtXWZVJZgMpkcdRd+M4COaF60JIZxLGfmmGFXWkeN1dKZpSJ58 SekJVkKuoiBmAT5YJ5jciVioMPoJmihLfqYzaaQJXqkFppYCAqmdmVa66ad4EuFmqPAlSKOcph7J KakYrnrpSE3Z0Wg7OS4x56qVyggoY2UyU2evVhUjLEq1EiXOsSxhFLuNsuQ5KxK0SEh7C7VnWNsC s/BhKw23gyaq7aumhosqrN8u66091ZrL6Z6ssvvQnYrCu1RY5F4kKID0btsmfunqEp9T+1YL6sD1 /mtwwgqjUvDCrSIcKcTBOkywxBUUAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032_image076.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC6VVTWgTQRR+Mzs722xjm00gikiZikh/jNCqR68pCvVgC70mYooJphUaCCsIPXvy LEi9SQ4KZU+Ch170Fjx4UE81KoioUDGearvOzE7WnaXRjQ1M9n15833zzZu3mdftF/dBfkq5kgUp ETmXkQiMxwYAhhMya/KRwr0II6QihH3fl9FZdEz9NhzOS+OSVcpleXSajsJx8MVkyHC8xaMnfLAc wIjFOWpOGubLjRuL7q0KwEMk1t7F5v4H6eGeWBQTDJkFt35t9SbApbw9cep7Ft5s/Gh2+GDsZ3Mr v9wmfGKBzx7iz1n7EZrDgjrh/kvvW97e7q+HQDx3IrrzppCYdBP4nPy1099noIuU7hhxkvt91183 7neMHE3ud+pvddX9btIB/HaS13eTDuB3ehC/X0cS+30/iN9iNuqX+fBHF4TuYrVeWWNXKk12dbVe Xkno94v5VOrOugHOWY58/84pvE58EHhG4RS+gAIc+Fjf/z8f8f159LYjJM67Pfw5HfXh0U9DUR8e fWAIfEZhRpxUdB+M6PkWeqXwAb7j513oJj5vjy5nhEQh9PX2iMDTIe4M6/nnKT2/Z+n5l7IvL4b7 0POM6PkWMmmAD+iLeL997CbuN4tWUXTdhqHjPdhQOF5PdKh+9Oj1UaGwEtZj29bxLtXxOBFXQrXW w3fk/8VciIuyf4u1Xv0UP8Q6nxGdz4jOb6EZeR7lEC9p/BbyNH4L5SV/qWarW8iWN5V8XSCoXQYs iZ7Juw1hfHLBXWtU6tAWdQLOGIe7kiC+Mt0sxM/MkPzfYp5qVXAHAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQFqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgAN AWAAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFAAUIDQUFCAgFBQUAAAsFAA0ICAAFBQAF CwgFCAAABQsFBQsLCwUFBQUABQUFCwgICwsICwsICAECAwECAwECAwECAwX/ICCOZGme5iOgbMsO hCvPdG3feK7vfH8WhoNPhkgohsikcslsMh8LobOEYMSm2Kx2y20Vj12gtEsum882MRnRAKPf8DjK EagHIA17IMK2H4t6eyNFESiAfggSY4YNQSJFjiIOkXKVlmcPjVIFAZFslC2ZboMJgo+lhS6fUpBj BRNXl7KzWJmpAHQrIgW3MgOwJZnAJF9Dmbq0ycpDnLqcAboIUTUOE4tswyUwxg29y9/gNJx/DAMB YA6jqgnWJLkoFIsmh0eZndeaPn0GFQ3t4QC3mDsyQMBAALxsrBohTN6NX2MceMPm8CE0AA8sdAvI MUs1AlAOfERwoSKLTJTM/3m7QWhQGyrsYpkLpAcZiYOSznXc2aRaBSu4rKW7gTLiRXd6/qEQNeJV rFPZcBxzp5Sn1R5FJhQEkHXAShlFT+k08c7Fr1iT5GV9eiMtKVBX4+IoAqEk1wR1TXrxZ9TmI77r PDXwe7eqjalNj8pdzDIPmD7qcBGGqZTTSltEBjN8SSWfiJk06/h1Sioq49MuMItQfVMxi4+kxo7A 2YL0Z8NcN+qAOIIOXNTAU9hdPVzbZG1RIZceA8jvpApRWqbQrGNcbgHdtgXfXqKATe8otqbm3Drp 0z5KAbVD3N102zrW7B3nTt/sfFJfacR74R7X7/oAkiGeC6/oFcp80sEUWf+ADAp0HykLepHAb2nx ZoIaDWbIxYCpTTPETPlVwZaGJDIx04MMYbBhhCW2eAZ4WXDo4ow01mjjjTjmqOOOPPbo449ABink kEQWaeSRSCap5JJMNkmDClpo5ySRGGJRzJRChsSFiFgCeSUXVXa5Y5hasMGimFYdEhosatZxS4Iw 6aFAIgbm5smEEf0HxzMB9Idmbab0pudmkQHyJiqZ3UmJbZZ49Zdsf/oCKUYqmmWaMGx9yQN7ciCQ AQkNRTpDNVJA+cCIZFWFDapSbqpbMmuJqsqrA5xJDDuLlGXCfizQg1EeoCy0m5uf9VknNbjJSoJ1 GBU3KyWh7mAhLhMBpoP/BkUIkC1T+iSQn7I56TFoMJ4BoBIPCZpJmUyh2TGZUxTEwGwPDzgL7q2R OPpkubqGC5+B3CJkWqw7TFKrJH62ZausrEG5752T5oTiWYKqFdMORVgQTbmghTafjPe25sapNVDU m2t/JYsvK9TdqvIMYSGEcg4whjwPric48GBWrgS62bcuIROwSym1K5oJFN+G6mGV2jzdV+agCJtY 6tDGAqPTugR0YKzgyUOV0hwrZr83TZycY8vF5hw/0Xl7AqeNCT1YvNV57DSfxiKN4tDFmkdMHumV sl7LyyYsA6PPLBzemks7bRwRbuvA6wlJl+CW44yB/MPLB/YauYKYn6b5/82Kr0xWEFk3NW7oAY2e goc+gGgIUKzLdeKTTcdYeu3B1TyF67wHL/zwxBdv/PHIJ6/88sw37/zz0Ecv/fTUz6Ce2Dk4jEWr vGsvEFvbXK4EmU1oyjr5Vhrxtr0+aLkFl7W7vwbtxLCPrvphrC6q+fnL4z0z+lOCukKHvveRRwQb uEYp2mW4u4RogXWYkyKe1TVKiK8SZItDH/KGsc/FyDDiO9iFfOafA7QpUHy7S6AMlagKuqKBYXDX JeolBJPpIIVNiFZThrEVT2ljUg/IXXgu5Y9M4Y9ehJNDMyxBJ0JJC4b6AJz/NEMH+LCFVKtZAclc gEWX9Id7N3xVJZbYAv/gTQGHs5lPF7GgM5yBSownYMMtRAi5qmRQBJOL4wLrASx8BHBxpjAH5wD1 INfJzlwc5IFE7GMINyIykImkGR8c+ZdxMYuGNBDWrwZpqYhUi5MswFYCtDVKNB5uZo9DgShJKQBT Wg+OlDuOJle5rQOypCQ86wznqmiHP8YMkVtbx5tsSbBHtutdsKDbvG5AxhfcB17yilgmIbi10f1S YARQpjT1E4NcuqxxrfhMMDdjQZTxMpLTcQOjoNK4URlAhFPDQTPDcx+DoQOKgEJlGpdSLv/AE596 g4rFEtYwFJGza9K8I3LQApdiziUBGqvkGDpGk9HMjKKBGEXGNgYKjNb/hJ9V8agfDkqKiNppESI9 2mqa5s3SNI42W3ylUjJoQ88JhjAtlYpn5slMfe6Tn5HgacFeNrqaxkyoNBBp4FSWU4U40jJPy4zc CsUxo100G5WTp08/8zGsAtQsgyqqIyuX1Q4aRpPkyo8g2xlPQFRtm4WTCW7k2EFFYe8HWzWXLL12 lz+u4z6um1o4+3pXCZ0VliebDJT0NcTzoE2garMc20zowc0YlBFyEwDdaEbCgMaxZcfY7GGstcgy dvUKbMisaM06xXclxSS+SyfSAnG2RF7vV8hsJ4Gykbjs5UGG9EQB4iKYgzYtzHXcGi5cnWqYdbLk UxIaJzz0UlZJ+BVLUHAywwVHm9cCZQ9BlT3F7sTk3TPw7yHjOq+EKIS6ZBUQXOrVwnszCbul1JcH h5wH/UInvy7A72sGDeKKhCfgMtAxB/k93GXxu2BlxTZGDwoBADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032_image078.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBw4GZgYuAEsQLDGUEM5khGBqCQDFiWFYg5mWAsJkZGKIuR6f///2CW HqMEVIwbro6HiYHJgVsIyFJj42eQYvgPUswgAOQfALK2g3jcDAzbgYZxQ9XwMPgmlmSEVBakMjAY gO3+zdTwD+LCCSBLGViYGARCMnNTixX8UssVgvJzE/MYbsz/XP4QiBUUvpY7SqTJsQDV6QJVcwBp I64FjBVgpxsawPjH2EBGmcLlbcD+0Yfap/CfPPsYGUD0B7i9Xxies4CMMMLmDyaQucGVuUn5OQwM HRJcJ888FcLpD4i5jHD3dnCAjNCG8/exgvi6cP4zJhB/M4a9jBT5ZwFjGzvIhDw4X4gFlf8EbEMy nG/FAOInMnBBY5cLnALAwQp1mwADO5i3B5xmGJmYlIIri0tScxnkQO5gAOpQZOiCaACCF8+FGNDD hBksAwBNNzAeyAIAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0032_image079.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhoAAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABQCa ABMAhAAAAAAAAAgFAA0LCwAABQsLDQsIBQgIDQsFAAAFCA0ICAUABQUICw0IBQAFCwsICAUAAAUI DQgICwUFCAsLCwUFBQsICwsFBQgFBQUFCwECAwECAwECAwECAwECAwECAwX/ICCOZGmeaKquwCAE RMHOdG3feK6XxgEgCdluSCwajynFQohsOp9Q0mAZrVpb1CtLwdB6mw3Hd/Vg7gaQgJrgiyICXZMi zR4iIuOUAV80qNViUA1/cSQNdXN8OFNmMw1BSAZdAxJDAxONVYOFImiFBjE5YTlzoURva206b3VE kiubPK0Ac5wtaQkUEKYkdyh+MJmdaYq/gCJ+vEZzf5AjwIHJwgCvKrEjLs63gchwtBUQ3NhZUhCQ CLYmb+IlFi4M74lQwLzuAvD38ifVKdfD2tmE+FH0ppiIUSXQBDqkSoW0Ewwv+BhkEImLAOIiTgxQ EVm6Ev5ohZMiIFStXspE4/iSNc2hmo5A9qic9QQNr5h8ENAkwQ9FyDniXIQCwiRgQkwJIXxUsS6F iwpx0Ghz+aeqmqXUWj2Nao4JMKt/KoZUWC7IyREhPZqgSAMNxxVznKV9okRIXCFzn2E96A2bAIAj GfrdOQBDw4M7T5RqyXMWqMNPHgl0nFgvrL7PeMkDxeTNVFpIQc5SkGHtZ6d/hRi1IrFTatenLVvD LOJsVhlsPYXrwfOjVNyxbXgaUas1EqIqFQ2vrdS4iZ4QMT6vw1blmgLMOBWGzPdYdLCERKsa9BZM 1WKCu3dUi4JZeEPXR4QAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

25

MSDs

•THM: If G= is MSD then

• •Lower bou= nd is achieved only for a directed cycle •Upper bou= nd is achieved only for a bidirectional tree

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0033_image080.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjA4IKTAxMgJYn3wY2QAMphnMTIwMDHIgGVZgZiTCcZiYmSEshiZ/v// D2bpMUpAxbjh6niYFJgOCAkBWWps/AxSDP9BihkEQLYBWcuAuAEoeQxoGDdUDQ+Db2JJRkhlQSoD QwDY7t9MrP8eg90wAWQpEwsTg0BwZW5Sfg4DAy8/17w/T4QYbsz/XP4QiBUUvpavFk17zQJUqAtU zQGkjbjqGEX5QVo1KgmZd0iE6zRu8xgZQPQHJHPVhUBGaELNbfjHgDCXAWRuSGZuarGCX2q5QlB+ bmIeTndCzGWEmtvAWCkIMsKwEsYP4wPxjSq5oPwCTlDo+mTmZRfD9YhxgtQoZML469hB0ZCfxg3l VzGxA1l+pblJqUUKcF0iTGBdpVh8gB4yZ848JTZkGhj7BUBG6JbC+Fq8IP5iON+PEcJHt5eRwpDr Bcd0HtweKwYInwuavrjAaRAcQdDUJcDADubtAadaRiYmpeDK4pLUXIbXIHsYgDoUGbrAGkDEi+dC DOh+ZgbrBwBKjyufSgMAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0033_image081.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwEgAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQAAwAG ARoAhAAAAAAAAAUICwsIBQgIDQ0IBQAFCAsLDQ0LCwgFBQUFCAUABQsFAAUIDQAFCw0ICAgFAAAA BQUAAAUFBQsICAUICAsLCwsFBQAFBQgIBQgICwUFAAUFCwECAwECAwECAwX/ICCOZGmeaKqubOu+ cCzPtPkINTwQee//wKBwCCsYDsQTIsFLOp/QqBSGUCCnAMTiiu16v+AXo/EtOMLSQYBcDrjZVEik qSoEzuhSIcLFaulEdm58em5ueD4IEm9fA2eKayMIEIYBhCWTcysMh12QloAADIhJnDglo1EPi0cm A61CanBTiqd2swCrmj12pFCrlZEiq6eBhsUjA7s/A8giancmZsa4UbcqirA5q75AzSSTp5Cw1092 zgDlPaYnAxOLztND6lP0Jtl9NNxD7CQ34BJ2MViW5JwNCd1icKqWTIAdgtM+4fjERo2ASaAAQEN0 CxhBUceSBRCgKxS0aCIE/xm6hEmCNkxymsiChGgfyE4aB1FAZ2Khi4E8MuWbN/KeSyScioJk2VNY im+cWMrLWWwhxgAVFhBYZeCbrJRYrSjaNYkNJwdXKyj4KmJSKzva7LV8OULQnKsCtrC1OQmRo7YS eI7wKYbQ2D5JT0Ud6sJgy0urGihqwBYcJYauJlIix1FpTjYPkWA8ZRPuFa5IvgHWFNrVMot1nSo5 iiKTTEtIbNocIwlCsX/3LseoBZhu5MmVYzi2fEmZhQRIP+4JpUI1zZSdi7FdPvA0QrBwbF8NRmZ5 b226rsgFSJcEUPCA8XAry5w6iekz9nin6xy6qI8vmNdWTFlA4MAFQUHQnv9tLaiWCzzpZCcSG8QM Btl36cgGVGQoCPigNgxmiFlxjInwnojxDSMBBoG5MkiJBQKIjVYjoGbZgQm215hnvWkCDIUt1iZc dcgI0sBUy+0V5H/e4UHPhksWgo6NA+6yniS0oXBiOYrIt0hGhbih44CyqcAbli/9qCIyJwXjRjw8 VolELxOyQFg7zqgRQQYSPiNMhSZe6KSGc1Ap5UEgEohiCviksKUwXaroQHonCDLmYGVm9lgfdPo5 IgseHvYfHd39lKlGzlzV52drWtgkfAMeAcksBZQXZxYB0eGWeqeimQ8FVzzKRqQPnqEGIghogKWM TWFWADpCubdMqTSEelT/X1gmZCY6DmKJ0oPiDAkok5LCuig0oBHiYU7ILnklieBYEWgTXGK4D0bD MpEMsycwgM5UWch7YoHtarvjlN+NewuC67RnE66EXDDBi9ztUhpuuBbziSGg3VpgUbuKJJiKLIVT Jb1K6WZvrjEmaPCObtrilMJrMDzDsdJEogwdRubsZkgiGdINwMCsAdtJEVDw5UhIi/YlgEkJtBJj SXm28a3jBaPJxgJU3dVKG0yNtAUanJSQSj+z+TNZS+4cW68rFP0mCW7nYffdeAeRChh75+3334DH vcUXkwVu+OGGn9kFwIg37jgYWsBIxBKSP2755UI8wEEXimPu+edCPDvFBAC4hAAAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

26

•THM: A stabilizable MSD exists iff

•        = ; Furthermore, only the directed cycle

•        = ; satisfies

•
•Step1: Ear decomposition

•Step2: Fo= cus on A i1 <= /span>

•Step3: Do algebra

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0034_image082.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhaAAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgBh AA8AhAAAAAAAAAUABQsLDQ0IBQAFCwsFAA0LCwUICwUIDQAFCA0ICAUAAAAABQsLCwsIBQUFBQsI CwgFAAgIDQsFBQUFCAgFBQUFCwECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZEkewmCubOu+ cCyTRDHfOG4ESN4aCZ9wOCIEjj3iCKW6ERRNpdCYlNZ8C0YjKnXyYAdGQOHQckVA1uO4ZYUDQdc6 YAOs2z7qa91bQBh1JykmYVAABlUsO4EmEQcSCI8IWXE5ei1rlTuVRYwiYXUEDRMxd2ciohMUpEac XoklWYkGeCRpJQ+1M3OuaAoPcbSkeV+Khp8Sx0sVZ2GwMIstjxBJhVFzR9nZsJcmsjTFJA/PrTJv vbEMx92W4SWpSxKjJQcWwzTzL1m6mPl2/u2eicgVZYcyEQuYmYCH8MLCgy4eHZN4agY7cEGcAXpw z45AawCeVLzhbISsVVPoHuD6siPAlizu6nUEd8RTEW043YX0ZwQOFjHbRvAJAQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0034_image083.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjB4wHaAkZETxDKIZGQAMphFGRkYmBhkwLKsQMzJBGMxMTJCWYxM//// B7P0GCWgYtxwdTxMBxgfsAkBWWps/AxSDP9BihkEgPwDQNYxIF7AxsDQBjSMG6qGh8E3sSQjpLIg FegOsN2/mRr+QVw4AWQpAwsTg0BIZm5qsYJfarlCUH5uYh7Djfmfyx8CsYLC1/JFnGmLWYDqdIGq OYC0EVcCIwsbSKthJYxvA3a/fiUW85lA5gdX5ibl5zAwZAlxWWU8FcJhPiMDiP6AZI8UK8gIXbg9 b5hAfFsMexhJ9AfEHka4PRIsIBPy4PY8AZuYDOdbMYD4iZVc0FDlAoc8OPigYSrAwA7m7QHHFSMT k1JwZXFJai7DYpC9DEAdigxdYA0gouW5EAO6n5nB+gG9c0qpQAIAAA== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0034_image084.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYwAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABgBc AA8AhAAAAAAAAAUABQsLDQ0IBQAFCwsFAA0LCwUICwUIDQUAAAAFCAsLCwAABQsIBQ0ICAUFBQsI CwgFAAgIDQsFBQUFCAgFBQUFCwECAwECAwECAwECAwECAwECAwECAwECAwX7ICCOZEkewmCubOu+ cBwThWzfOGkESD4aCZ9wSCIEjj0fSkVsCo3JHM1JlfJMB0VgwVA0mLrgynH8NsmBGoBsfl5J5N4D olCfUljFQmWICiMHEgiBCA8KYj5QcAGIO4gjUyVZagQNEyZoR5qafiKVExSXRo84iiKGfgZtYZir VQYLDmKql25RsGCBe5IVYCJZnU6BEElZuyOZm5wlpqhFb3DBo1Ujhsemtp6WI4HbJxa1Rd4uycrQ Ig7j6eGJb+lgO8fVvSaf1RdNukz6RKbTwHUcsHMQDIAxFQTkCQFWTQGCUEOM2NkR4IuhcwfAsTBy xE6/cRxJ2bjIKQQAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0034_image085.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+2dT2hc17anjxP7pjsv6Q5JnNhYoJuO0nqeCGOEiUbqxumHCXkoN7ohxsnA4GD0 cE8EdtwIQjd2DYy4GakHSo+Kh1oQJHoiMBoINHBoDfRaiSZqoZEQmUmDHshT02vVzq4cH5Xqz6mq c/af7wefVCpJpdI+e6291t5r7/N//8///h9JTZNn/nrmn2qP/utXZ5J/nSSv/tPlP8lXH/7zK/Lx vbeS5N//6d8m/+7PX/3jP1w/U/u5M8n//Hv9PKYf/pwkf/vtT8nfzr6W6Hf/c/KHJuWJv5754+tL HyTJB4PyK//pH/9BX0V/59Xa62V0TjibJP9BvvH/st87OJv8t59eTf4iD9+Q3z/tb1npc18Kn8tj fdP/Rfjvr5rf+3PyL/Xv6/f+8vvjM/pPpX4urRcvXgAAAAAAAAAAAAAAAAAAAARN41oBo3qtwM+m VoD2AgAAAAAAAAAAAAAAAAAAiKRWYIFaAQAAAAAAAAAAAAAAAAAAgKhqBSrUCgAAAAAAQO84OjpK dnd36zx79ixZXl4+wYMHD/pK9u/p+0i/L64VABTtF7e2tuo+aW5uru6v7ty5U39cqVRe8l2rq6sv +S7L8+fP+/Z+9bWzf0/fh31P1Wq14XvX/8n+jP7OwcEB1x8A2vaRNmZUP5j2L2m/aH1SiP5F/6f0 WGHHCdsO6nv1ef2+thl9ByAu0n6ykY+0MSP+4fT2s/5V28y2H34VqBVIkr99G2etgNq99QvZmAuf 2p85hkY+uN/zGwDQe385MTFRj0Gx4fL8ql4THbPUpyp6PZiLBXBjfk9jSZ3XU9vEX/rhU3W+xV4z 9a34U4Di4kz1mTZPVDvUr7FBf9EYFX8K0N9Y0+aB6jvVZzJ/Ga4/teOjxqrkEgDdxSY6n6mf9Wva Ja58X+dkbGzKmAnUCpxSK/BJvloBne8k/4MsGrvacRe/C3AyNtE83s6Dsp8Rmo2xdl8WvhRYRzqq x5zqQ5kjg058qR1z8aUQY/+3ezI1R6NNoJsc39al0h4QQ9xpz8ggX4d+rFPRryBU6ONQ1Bita5HM C0FINaBF5Fpt1QoMcQ8CeBm7lsnYDqHEqdQyQRnxK3Oq4PNclq4v6foq7QFlYs+3Zh4AfBv/WZsH l/bRaS0/+RD4ME9KXwWX5/AZ2wH/CZB/jsmeMU17gIt9Mwb/2VatwFlqBUJB5/SZ1weXYB8T+Fhf gh8FV9ZIFdoCfNx/ih+FsvfTawxKWwB+FKBzqLUH8nqA/OM3OTywzgSQPwZ1ZZ/I7Oxscnx87Hyb 6fvc39/vXa3Ab+eoFcDnQgTxqiu1e+rDNjc3e/Z6Ozs7NfrxXnVMmJqa8mJsiNmPkotBv9EafRfO L1dfNzMz0/PXnZ+f79t7XllZ6evrA3V94P4+J1fyHY3pehmDWtbX19vOz/OgOjw8pD85vBeFtVXo Z+2oC/dUVh+kavQ99asan6qP1c8231da5dGLi4u1103n8/b1avOWY2O1x5bJycna8+p3O5l/0HiU /uT+nmjOkYJ+5PEuvA/1Weq/GuXK+nw2ztOfb8fX6fdPmx+wfrnRnEKj55vl8+pH6U9uo7GCxqO0 BfQKnQPV80ZdeC8aL2Z9ncaYqtNiPPWt3fgufV1Vo1hWfW+7a1H6s5343NLPFfiZWgFqUqGMtXu9 14Mr/jbrO9XfNYpLdR5UfbPm7Kq8a1b29dPztem/1e66kv6Ovhf6lB9ojMF6FPRq3tSV++Q08qHq K1X6vX6uHaVfP48/xoeyHgXx1oe48l40B2/kv+z6UDuvoT6307V6zddtLGvXpBq9RrPX1vfuSt4P 7a9HMY8Koaw92by60fqTXYNvVmdkc267Nt9p/JueP9X30WhNq9lr69+nntTPuVFq9aGbfMa1s58a +Ur1bRqLNvNRNo+261WdxKLqGxvVSdnP9vlmr92vGlgoJhfjvs+QB+03rt3HQf1ko/V6u/bTaE3d zpla32trTTvZ23lanUA2Jm302vp3Y5wLbatWYCGsWgGteaEeFULxt+r7NPdvVMNk5wWyObn6aPV3 Nma09aid7EeyewIazYmm/XCj19a/30mdP7hZj+pK7SD4NW/kwr6nRr7ytBxffavOdVqfp+jPa9xq 1+HtPEG7eXi2nspi16XS6/vZ1272XsG/2igX7QHc9qGuzhmpb/LhjCXmS8NaSyCnh1B8KAA5PeBD AVjTB3wogPO1ApVyagV0Td+le1AA/hbAR9twrb4F8KEAvu0NdOH+EoAPBfC11tq1/YGADwXwCT2/ lPpSwIcCUF8K+FCA0msFvm1eK6DnpHO+FDTCpXP0AVyGM6PhtPl1aj0AWIsCfChAEWtR5G2QnVtn bAXobC2K+lLI7jmmHQDag7NOoNFcOe0A0D7dnl/aVq3AJ2HdgwCIWQHywFknkPWhzAUBdAb1pUD9 PkD38Qe2A/hQAHJ66G5fE/WkAPnthzV9avLxoQDdremrL/XyXIEhagWKzl0YcwG6q+lnnz7z6LQD QHe5HzXc1O8DQHdrucyhEYcCQHfxCDUx+FAAyL++wNn7+FAAyI/u0Y/JptqqFThLrUC65oN9pAC9 Q/eXMo/KHigAYB4V8KEAzKMCPhTAz3lU6gzxoQDQnX1x/l7489/4UID+1sm4uFc/uFqB3846XytA zRQAe/UBHwrgMuo/OfMUHwoA+eHM03Br3mgHgGKYm5ur3ROKtiAOBQDmRpmjOaiNi7QFQLF2R62+ x7UCP+erFeDeJQDlwP2gw6kr1j0atAVAOXNu1HxTtw8A+ffqUxvF2hMAUBtFDRQAlIWr94OG1nkE 4x+AO7VRnLHuXw6Rd02+rVqBhbPcgwCgD+gaBvNwrD0BQHf5PzU1zJsCQP78n5p+fCgAUKcfw9wL 1wmAOn3IP9ZRdwHg7j591pfcn7v24TyatmoFKtQKQNzoeUTERMybAkB3tai0hZs1++QUAO6jdeHE omHV7AMAsSjzLHOsDwIwLwpd1FjQDgDMvQHrSYXWCnxLrQD4ESNxJoo79Wzc7wmA9Q7IX7PPfWQB WIeC/HPZ3EMWgP02wNoTAPk8sPYEAO3m88RAXANqBdqoFfiEWgEgXvIdrdcnbwDwe/6Ueqjy0Psc 4EMB/N6Xz95F2h8A8tsw93zChwIA83H4UADAh+JDIeJagSFqBVj/APwtAGDDtD8AYMO0PwC4tAdc 9+DQFuXAWVAA7GkC1v8AYkT3MumeJtqCawCR1QqcpVagjJyT+0CVz8TEBO0A4GnOz7xp+XAONAD5 JnRXz8s9nQD8i33I48kJAKBzuJ+TmzWlrOUD+GOvxKDujWu6tkQsCkHVCvz2atS1AjpnSrzqJjoG VqtV2gKAOVPoYg6V9XwAN1HbJAb14xqR/wO4ueeeczP8yOmpiwJwb/8Sc21+zblwvQDcWkciP/QL 3S/B3DVQK9BGrcDPbtQK2BpT8n1/64PxuQDl5o+ckYkfBYB8NfqsY+BHASDfOrCu2dMW4fhRHQ8Z EwGoR4Tu5mbwowD99Z+6n1vX7WmPcGvaGCMBSqgVWPijVsD6WvYgxjGvw35TgN7OrelcKTYV3/wO NRoAvcn18Z/xrktpnX9R8wCbm5vJ5ORkLR+anZ2tP7+/v5/MzMyYPGls7KXvAbRifn4+mZqaqvUf /ax9SbGPd3Z28J/QN/SeJtoPitx3oT7y8PDwxPPqP9UeuC7QKcfHxzUfur6+fmLcbvQ8/hP6sVe4 qDP5tb9rfNDIBlZWVrgmkAuNOxvlMDouq7SP9bJWlLV6aLQPo6j1Jo0LsnlXP+IFiIfFxcVaLtOo r6l0zqhXa7Jl1MG0VStQifseBL6uTRURv6qftXGEzm+p+jXPBeFjc/y0X7X5UTZH6mYPDDWH4Er8 qv5S44xexxUQ9/yp5j+a69t1KV3zbDRXT80L9Btdk9K+o2ei9mvstWtROmeq6qavA6i/zM6fat/S +YA847Ndn2WdCbrdN6X9SPtTr19bfab2eY1HVbQ3dFsTpX600dqUkicXI3eHXtWeat1ps7VL/RmN XTvtcxonaL9vtHYA0Om6ZqP1+vQYrTFls7hS+7f2c+5JAf3M79NrTtvb27U4dWRkpNZP9bN+vbe3 11EO1mmcANAor1Hp+lL6efWJV65cSUZHR5PBwcEa+jh7vk8ZtdVenivwLbUCRcav6m+1X/7000/J 8PBw0kjqd9v1uWof3a6zQtzoeqbdR6fjd7oeb2hoKDlN09PT9ZysyP2AAJofffDBB0kzjY+P01ZQ Kk+fPm3aR997773k448/7svaAECrOYBW0vyK+4JBmWi+1EpffPEFbQWFo/NO7QgfCmVi5/SbSf0s bQWu5Uj4UHABrQ3Bh4Kr86HN5upVb7zxRrK2tkZ7QWnomlErPXr0iLZysVbgE2oF0mg/babHjx/X 6vdir0OB8ub3v/nmm+T9998/tY9qzMA5UFBmTZTGBAMDAy/1ywsXLiQPHz58Kb7VuVat/8OXQhG+ U/ua9jnte1ob3Si/unz5ckf10QD9Qvuo9leNS/XzaX4SXwpF+M5G91jS8X5hYaHeR5eWlqgbBWdi 0U5zIf15uycVXwrd9j97tqiNO2kX8Antv3nPG0vHDfhS6ASNM9Vn2j3N+E7wFY0nu+2/6j/J8aGT mFP7Xa/2IeGDI68VGPKjVkD7fy9r9uy5PfhdKDI+1b528+ZN2hoKR2OGfpxTxnwA6HXXvmXnRPu5 T97uh9Z1VNoeit5H2s9zxm38gS+NZ0zW6625Tb/9Zjafevfdd5MbN25wHaDwHKuovVY2l9O5M9o+ nD10ej11HlT9psadZd37Q/frv/3227W90VwbCNnm7H0i9DO1gH76TBtrqu/U+g8X1n70/MfamsTY GP0KoljLtfeaalb/D+XPaep1Ul9p1931axevV/rsvewZ+wA9qRU46/+5Arbequy8Mfbxz/pWOz9j 76GkMaoP1yR9PorOARC3Qqw1iTY+susX2EJ/fKX6R/WTPvrL09ZS00qfIwHQa3Te0nVbsXU01s59 t/Ei2836Sb3Oth7N+kp9TtsxtLmW7Jm8evYJfQX6hdqTj75B7d/GqWmfYOfzQrYZXeOx/lH/Z9sW af9oz1BK+8lY4vhG99fhfGjoV+2T2l5Iuan6C/Ubtm71NL+SxvqYNL1ci7bv7TRsnGixMXea9P+g 18z+rM5x9Pr9htCv7dmQ586dq9+TbGNjg/aBnufxsdVzqn218mHpuK5XZF+/lQ+nf3bHtWvXar5T xx6dD9V8/urVq7QN9DyPz5vftVUr8Nsr3IMAnGd0dLS2fm/3YalNFLkPC+KJWWkHCBGdK7X7n5g3 BQDojPS5PMSfAAD5sfk8bQEAkD+3px0AAPLvcyKfh17hU+1TW7UCP1MrAOT+4GaNu497ngDI/cGV eJX6JyD3B8iH7uvhXAcgnwfIv+eJdgDyeYDOsWfT0RZAPk9bABReK7BArQC5PwAAkPsDAJD7AwCQ z0NocNY6APk85ENrRxl3AcjnIR/2Xpy0hSe1AhVqBcj9wed6fe4lD0DuD/nmTEO51ygAuT8Ujd5j k5wfgHwe8seh5PEA5PPQHvhLAPJ5yM/GxkaytrZGW1Ar0LpW4FtqBcj9odsxeGRkhNp9AHJ/yOlD VU+fPq37zunp6eTx48e0DwC5P7Tg9u3bNR/60UcfJV9//XUyNDRU+5o4FIB8HtrLS7KifwCQz0N7 jI2NveQ/NQ5lXR+AfB7a49q1ay/50KWlJdoFyq0V+CSsWgFyf2jkbzV+pU0AyP2hPfQeeVaDg4P1 dXwAIPeHznwoYyoA+Tx0xsLCQs1/XrhwIdne3qZNAMjnIUct/q1bt2gPAPJ56JBHjx4lb731FrX3 EGetwFCxtQLk/nFz48aN5P79+7QFALk/5ODevXvU6QOQ+0NO9Nx82gGAfB4AoEz0XpK0AwAAQHN0 vV7r8JWDgwPaBKDftQJn/6gVsLansBYRLnptHz58WD+j1O4b1fVH/C5A5+h9f/Q+FGnp17onhvYJ D63PP0163ak9BejMf54/f76hPWls8uOPP9JOAaFnlLSS3oOEtgJoj+zZv1lxFnBY2HuONNPo6Cht BdAG6TOAmonz1cLac9FKej4pbQXQOx9KfSlxKAC4EYe2VSvw25mg7kHA3CkAKNm1+6wuXrzImm5g XL9+velcOdcboLO4hDX8+GpJv/zyyxO1pFevXk329vZoI4AcfjQbj6p94T/DRmvvtV5Y58Z1Dog2 AWiNnlfS6MwnjU20rlTtaW1tjdonAIDMnuuvvvoq+fzzz2kPaDtOffDgAeMpRI/m5JcuXUreeeed aOyhrVqBn6kV6HWOo+eJsT8fYkTvJ6lrCqo333yzltfTLpA3dn327BntAdGs0ep5P3pfXqsnT57Q NtBVn6pUKkm1WqU9IGiWlpZeqm9Rae0gbQO9YHl5mflUCBKtAWxUZ80ZafGws7OTzMzM1K771NRU srKywhwpQBs5lubp2dhTNTAw0PX+z8nJyeTw8DA5Pj6u2aWyv79P2zuMSv1pv+dI1Y8yRwq++8/v vvuutj6vZ/hcuXIlef311+s+VOdEu/0bGtcsLi7WbNLapn5N+3dQK7BQbq3A+vp6Mjs7m2xubpbi b9PzqZyLA6Gss+rZaupzVePj4x3Pb2ksqjGq2qaNSzV3rPmOsbG+5ZHQOXqN1E/Oz8/X8okyfGh6 PlXjV+ZTIYR6P50rHR4ezjWvpbGo+kpro3Y+TqX+U9H4R+NY2r1c9Dro9dDro/MyZfpQ2we5JxT4 iM5d2RhA15lUee/FZP2l5oeKjW+sTdr1DY19aPtyUb+pOUNZc6fMp0Jo/lO/1vMo7t271/VcaTbO 1K/J491aq1cfqjlDei1Qxz27hl/WGiFzpOALWhet/TQ9B6VxaN45KbU5xcai6fxQc3zyd3fQ66TX ROdbXB3bmCMFl1Hf2etxXvN2m6NrrZNd77X1T3aeFByuFag0rhVQP+t6/RrzqRCLr03nk+pz1Taz axoAzKeC7zWm9EXIrkH5MKfNfCrE5j81P9Q6G9re/TlUnY/J1pK6vIef+VQoGl1TKvo8M503Pa3G BoA5UvBtnxL9DZgjBcB/QiC1At8We64A86nQ79xIc318LYQO86nQ7z1NAMynAuA/AZhPhSLq7PGf EHO9H3Ok4No+JQDmSCHkcRf/CdQKnFIr8El7tQJ6DhrzqcCeUIDu9q1gI4D/BCCvg96uVRa9JxTA d1ZXV5lPBfY0AXSBnSPVz7QH/hMA8s+RalyazfmJUcOus2efJ0Dv50it39TPN2/ezFcrMFTsuQLA niYAX+dTNY7Vr1UPHz6kbfCfAJBjPlXPxB4cHMx9L3NgTyhAzPOp6kNV58+fT9bW1mgb9oQCQBP0 ftaPHj2qxaGfffZZzXdaDQ8PJ3t7e7STp/Pieq962gOg//Hn999/n1y8eDFppJGREfJA9ikBQBu+ dHp6OhkaGjrhR8fHxwvxo23VCpylVgBfCxC237179y7t48GeUD0PnPYAcMeXfvjhh3U/+sMPP9A2 7GkCgA5rpG7dupUMDAwkr732Wu1sVNoF/wkAnbG9vZ18+umntXj0l19+oU0c2hNq91IAgPv8+uuv yf3794l7HNmPRn0FQFj136Ojo8m1a9dqaG3/0tKSc++zrVqB3xJvagV0PLt9+3atZk3bXT9rfk8d MECYaN3/aWJff2eon9R9vI2k+yl0DoZ2AggH3WfTTLp2tbGxQVu1yfXr15u2p+YCtBNAOGhtfytp XtpNnXmvayR7XbOuuXcv5pP1NU6LQdNiTAIIB52vayWdy8v7+rpPp5e15ho3VyqVnp3zYc+BSZ9N 2E3dWTvijBKAcNA1p3760F6fq2nrL3sZi/bq7KV2fShnHgKEg+4ZbaUnT55E1y5t1Qr8nL9WQMeU Vnm/7u+l1hQgrDVnXVvG5nuDjk3NdO/ePdoJIDD0zGitd8zq8uXL1D/mQM9A0NqHtDQ+1f281OsD hInGmjqnp+v1ij7G3rvbt2vP6NbPrNsDAAAAAAAARFQrsJBwDwIAAAAAAAAAAIAC2NnZeanOcWZm hnYpiMnJyeTw8DA5Pj5Opqamauzv77f9+/q7er1U+lqLi4u0K0AJzM/PJysrKzV/ig8tDm1r9Xt2 HNPPefygns23ublJmwL0GY1xNF5Rn5m1ObVn/b7GRLRV/9p+dna2HmvquGXPJ9XH6Z/Xn9Ofb0T2 2nXqQ9uqFahQKwDQDRoPqdSnqs9N+1Z9rHbbSd4JnbW9PfdZfWl6zkV9rbK+vp4rZyBmBSh2ntTm +Dr3Zp+3dq7zd7RV/9pefZ1ixy+b79s5Fx3b8KEAbs/Xae5ov9bYx36tvjX9Peh922fjTP06m/Pj QwHcnLtTNPZUpXN2jX2sb7UxKfS+7W0sauN/G/vnXfOzsav6UK4bQH+xc6B2Pq7b2Afytb3OldiY 0dY/cX88AH/iIbXlTmsWoTfzobbt03Fo9OcKfEutAAAAAJy+b4a8v7y8Qdf8aAsAv+1Y5+uo0y8e nTelTgIAAAAAAAAAYqatWoFPqBUAAAAAAAAAAAAAAAAAAACIqlZgiFoBAAAAAAAAAAAAAAAAAACA qGoFzlIrAAAAAAAAAAAAAAAAAAAAEArfvGJqBf7X2ca1AlonkCTUCgBAOfwb8T/v/u6T3vr9sbql V8/8q+ScfP67V/Q7+uiNV/56ZvLMh//8SvIf/+7Pyb8kX575a82Z2c9/L/zljH6tXu5C7RXPfnIu yeoFQigmYfMIYfMIIWweIYTNI4SweYQQNo8QwuYRQtg8QgibRwhh8wghbB4hhM0jhLB5hLB5hBA2 jxDC5hFC2DxCCJtHCGHzCCFsHrWho6OjXatnz54tv6wHPVL6NeWv1P8i7Y/No76Y9NbWlrG3ubk5 Y4R37twxDyqVSt0aV1dXd1/W8+fPu38P8iLp15S/Yv5ctVrNvBl5e+Zb8mMHBwdcPmwetbBtM1CL GdcNqW7Sxt4cNyR5e3UPZdyT+S/EO8gz8rz8m1xrbD5G1c07Y9tmoA7PMOqOQP5N8//iArD5wMdw 0+PT416o5t1+spBxAb3KRBA2X7KRT0xMmDGcPt3EBUhziR+8U5O0FXMB2LwHkm4qQ7cksdJrMfJu 7F+yHtOM4gUwfmzeufFc7NwEqNJN5TF9tIeSwR/jx+ZdGdJNICrWLnbORFQBxm8cq4QAhE7YfNHD juTn8lEe0yDFh/2SMZlhHz+LzfdRkpYTYTolGe2N58XysfkejyoSt5tEnSJTN32xqfzD8rH5biV9 yAzsYvNkj+5bvvHLWD42n7MDmbpXiR658H5F+2Zhn6bA5jsY280uEcJ4f3MxM8PHFcTmW4u+Epjv rlarJGXYfGMdHBwQE4YnM/mKE8fmGw/vLL+FOuDjzbH5l3K/SqUyNzfH1Q1b5lQP4vzYbd6MAMzM R6Ktra2JiQmiuXhtXq49PSA2mVkbvHyMNo/BRysJ783JHDRFRDZvrjoGH7PmaqIdYrF5quvQi9pi DWYfhc1Xa+Jaohe1Ql3MPnCbNxuwuJAIs4/F5im8QQT5Edm8eHSietRQTOmFafMyyBdThjU7O3t8 fFzWvyl/fX9/n86K2cdu8+ZeMcWY3ObmZr7f3ampyzcg7mZqaqpEp+O12RMJhmPzExMTBRyfIhY7 MzPTzSvMz893/zZWVlZ68joRinXcQGz+4OCgmLBNBtjcg7zR+vp6TyLzJEkODw/psp1Ksj8mekOw eQnYCjiRWmxMLC3zpLgAGfnFF8hHE/aLTgu8FxcX5RXq4b35XXlmbGxsxmpyclKeEdfQMsWQ0Z4u m2+EkKiQHXh+27xcwgL+itihGGQmxpZn0uOt/EwTi5XnT6YGxmVkMojMMw3DezF7umw+yQghoz3t 4KvNSxpfqVQK+EMySqctVgZzMe+Tg614gY6sUV5BXicTGoh3aD7bJz/Q0i+gJmLR3mObf/bs2erq ajE2nzZmscnMkC6JujgFCdTl+fan+szr1KcJ6i/YfJZOfkz+EF22G8lQwXyelzYvyXwxx6FlbF4s XGxVnuxBu6dep01ngc13L+bzfLX5wgrsJQjPGKSZe2vyK/s1tXxlidJNaGCm9DK/0vBF5M0Q23cv c8YGNu+ZipnAM0F4Zg7PzMM3XDMzkbmZmW8ngqin9PJXMlOADV9kviaMtieJfcyFOv7ZvDkeo7gG etnCxUplqG9oeybwNvN8LYd6serMGp75aJ5p+CLdVwqgdKgY7WnZ/tm8XKoiT0ES885M1JsZuMwc u0n1jXcw6/bNX7bhEkB6wM+8iLwyyXwPdXR0FO2KPTb/oqVxSnifWVczMX86IBfXIDZpxmGzYt+y Zs5U9WQy9roXyLyIvH7Loh3Ukba2topZ8cXme5CMFVCBl7Hwk8G8eAHJyY3diuRnZKg3U/Em/m8e h6dX+IzMrF59Mj/9Ig3fAOpeYvMF9yVsPqfNF5+JidWVuK2NNL5Pktg+wggfm0dE+BVsHptHESm2 OXxsHsUuc7+zeCJ8bB4h7VTx3AYHm0dIVcyxS9g8No9cUTw3SsDmEfpdc3NzMSzXY/MI/a5Iluux eYT+0OrqavBb7vyz+cIOyUFxKvhDNdhjg1C2g4U9mYfNI5TV3NxcwLEkZ2Yg1KCPBbxcz3l4CDVQ wHtvvLR5bk6AClCou+sZ5xFqrFD33vhq85GURqNyFeRyvZc2T1kOKnKACayzYfMIxRXh+3q/Opbo UZH9LaQ5fC9tnrIcVLBCurkl96JGqLVCurll4un7ZrkOFR9dhlEY4qvNU5aDilcYx+YxziPU2WDj +5oRNo9QBwrg5pbYPEKdaWtry+vu56vNVyoVym9RWapWq/4m9r7aPKV4iMQem0eIxB6bR6ifib2P a8bYPEJd9UPvNtv6avPS0Ng8ckEPHjzwqxSftTqEupJ3pfjYPELdSgzeoz322DxCPZBHe+zZY4NQ b+TLnTAY5xGKK7H30ualWcWn0smQgz3T/UIdzsZCqJdy/3hsX8+9DfIGIygMOX48tpc2T0EOclmO H4/NvasQ6r1cXrrjHpUI9UXOHo/tn81z0DXyQmbpzsGTXfyzeW5ig3zR7u6ug3mofzbPBB7yK8J3 bY3JP5snmUd+RfiuVelg8wj1V65V6Xhm8xLVe3csCUJOVel4ZvPiMoO5PSiKRwcHB+5M5nlm85VK JYx7g6LYNDc358hw5ZnNk8wjT2WW67H5znR0dETVLfJXy8vLLgz1Ptk81TiIoT4um5eMiGocRFYf kc0T2CPf5UJ+6pPNM4GHApDYfLkbb7yxec7AQ2Go9Gkpb2x+tSZ6DPJdpc/keWPzMshTjYPCULml Zd7YPBN4iPA+LptnAg+FFN6XOIYltBFCUY1hftg8N7FA4aX0Za3Y+WHzW1tb2DwKSdKfyyoqTWgg hErp0mWdk4fNIxRXuorNI4TNY/MI9VklTlFh8wjF1aWxeYSweRoIoT7rwYMHZd3owg+bZ1MdCkzU 4bUQdXgoJJV7b+WENkKo+Li1xFPxvNlXNzExQV9BwQT2Jd61kjMzEIoraPXG5re2tjgPDwWg0o+7 9uzcW6fu441Qp3LhthY+2fxyTfQb5K9cuH2VTzYvPnJiYoKhHvmbyXPvqo4lPrJardJ7EJl8LDZv snom8JF3kk7Lvai7ajsifOSXHjx44MiekcTH5pMAiXU75JFWV1fdyUkTTxtRbJ7EHnkhM3XnTmSa +NuUlUrFhRkRhJrILMg7tRM88b01MXvkeEDq2jbwxOsGxeyRy1peXnZw4inxvVkxe+SmpE+6ecO1 JIDGFbOfq4l+hhyRyyvKSTCtjNkjdwx+YmKirNvRRWTzL2qroJTrIBcM3uVS0SSwFpckiuJcVGKa KTm8490vCa/dTSrFObmIET4Wm39hZ/UqlUpv4/zNzc3JyckkSWZnZ80z+/v7MzMz8szY2Fj9SeSs 5ufnp6am5HrJx5mazIOdnZ1IDD5Ymzfa2tqSy9DzEiix7cPDw/QzYvDSmbAoL3R8fCw2v76+nnbl mWcCNvjAbf6FLXXu7ek60mlkZMj0oZWVFczJF8nYngnKxGXLRZRLmePVzDq8s7P00dm8kdh8byf2 ZExIB4ddjhKoYC0uLkpolrmgchElU8th8N4tFSWRXGYzsdfDAV+s3QwLkgpKd+k+IUSFyQTzdQs3 gVs6dmtH9Uow79aGk6gudg8HfDFyGS66GSJQuSm9BGjzNcmDycnJzBxNO0OIp2tDSWzXe3d3V65W tVrt3j2byTzJ5KUDddRjUOkSI0+n9HIRJdpv03GbuWF/a0CSOC+5eGi5bHLxunkRsXPpNzLai81j RX5Jhncx+/QzUzW1GSp6XesZb2eVy1apVBrOuMq3JBxo57rK+CBdJzMhhNyXycjSE/V1331Q08lf kX4ivSWA05liH6BMqF+f29ve3pbxf2RkRC6/fJTHe3t7LaPEdsYH5JQkRpNLvLm5WX9G7PnKlSuj o6ODNcmD9JatPtV6YPOlDfhi83JFf/rpp+Hh4eRlieU3N3vpN51O+aJytbOzY6onxV/XF1yHhoaS E5qenjbxYM9rOrH58iWR2wcffJA00vj4OO0Ttp4+fdrw0r/33nsff/xxl/M+2Ly7QX5yiiTSCyOo Q6dJorzTrv4XX3wR2D+Lzf8uSd6S04XNhy0zg9NQ4g6w+biiO2w+Bo2NjWHzMebzDWdxRG+88cba 2hpNFLCmp6dPs/lHjx5h88FKrm7Dq/748eNqtRrMUg3KSC7rN9988/7775+89DIMeLRhDpvvWM+f Pxd/PzAwUL/kFy5cePjwYT0QkJzfnTsNop5Yu1xQuaxycbe3tzOB3uXLl1tWZ2DzIUiuvXQCGfPl 40nzxvJDsvbM2XXi9BcWFsylX1paCvUwVWw+O9S3E8vJz5i6XSzfu+trdrybsT3ORsDmX5J0iPY3 SNbHCizffcl4LnZu6qyjtXZsvoFk9O60Q4jBE+27P7DLlc1XTheej8DmX+ofuRdjzaYrLD+8gV0u 6M2bN7H5MCXjQJc7JYn2S5e0vFxEk7H3pE7eFGVvb29j8wFKeklPDj8xIwyWX7C/ljaXMK1Xpp6O /t59990bN25g82FGgz18NbOqx32y+ydpYWlbSdTF1GVs799hVSMjI2+//fbTp0+xedRWvzSnKclH bp7ZKzs3Q7pY++rqagETbOPj4+ZWRWFcQWy+CElfMSfwNazzQS0zamk9sXAz/S6PC27D+k7bMG52 js0X3X3NGNXXWNR3/2iM3GRG5gg6GdtLbK76DhwJ8gMY6rH5crq1SUTr08vRhv11CxfDFvN2xMgz Sp+tUN9/gc37LUm2y+phZm3JdHfX+nrP/1Nj3tLaZkXTWLh8Kf+1yylP+myFoaEh3y8QNq+SzueI VYgBmPG/bg8mffWinx0dHRnDXq7JbEkw/4jZvlY3b7/imsy5ab6fooHN6xKd9E5n414xEjEVs+B/ 0oTqMrZUV+7ZbPNHT8qMz0YmMKmr/pakGc0PSLbSzXtwsIeYHdbnzp0z5yNubGxg834H9j4uoUtH PM0m62NsPi03UsanxNZJrl27JtYu3k3yeQnvr169is37Hdizco6aa3R0dGRkxFT7mTvS+nsANjb/ ooc3qEahSnJ4U4cXwJGY2DxCrVXffOX1CI/NI9SxTHiPzSMUV5yPzSMUkXwP76O2eXa5ogjD+3ht /vnz546U3yHCe2y+oEGeVToUYXgfr81XKhV2s6IIw/t4bZ7AHsUZ3kdq82YHKx0XRRjes1aHUFzh PTaPUFzhPTaPUFzhPTaPUFzhfYw2H/ltSVHk4X10Nm9uLEVnRdGG99HZvDlbls6Kog3vo7N5TsJC kYf3cdm8ZPJuHnGLCO+x+b5odXWVwB5FHt5HN84T2KPIw/vwbR4jR4T3cdn8xsbG2toa/RIR3sdi 83IxRkZGMhE+3RRFG95HYfNJkpgbEoi1T09PP378mD6Kog3vw7f527dvi81/9NFHX3/99dDQkDxm nEcxh/fh27wEXekbCVN4iyIP78O3+bGxsbrByzjPND6KPLwP3+bNXYSNlpaW6Joo8vA+IpuXAZ9+ iQjvA7f53d1dY/CDg4Nm6h6hyMP7WGw+gNuGI8J7bL61FhYWxOAvXLiwvb1Nj0SE9+HbvCnIuXXr Fn0REd5HYfOPHj166623KMJBhPex2PyNGzfu379PR0SE97HY/L179yjCQYT3Edn86uoqXRAR3kdk 8wiVIpfveozNIxSXwrT5o6Oj3ZoODg64xqhg7Vq5OZcUms1LKz98+NDskzcltxMTE1g+KkYbGxsj IyP1PV3yeGFhAZvvr27dupWckDQ9S/SoAIM/f/58pu/JqPPjjz9i8/3S06dPk1M0PT1Np0R9Vfqk hrRcO7UhKJs3x2A11OjoKJ0S9TWHT06XU3s6g7L5zDFYaV27do1+icqyeaeW6xnnEWKcJ59HqHOl Z+zTunjxolNTyKHN21+/fr3hJArz9qiAIYd5+xL0/PnzL7/8Mr0+f/Xq1b29PXokKsbs06O99EPX DP5FqHV4BwcHCwsLc3NzkmXREVH/tFVTZtTZ2NiQvre2tkYdHkLhSLLFr7766vPPP/funcdl8zL+ P3jwgB31qEtJxH7p0qV33nnHx74U3TgvkdidO3eowEf5tL29ffXqVcnV33zzTYnhffwXYoztzWj/ 7NkzejBqX2b71oULF8z83JMnTzz9R5Jor1+lUqlWq3Rl1I6Wlpbqi0Gi69ev+/u/RD2Ht7y8THqP mmtvby9T9OH7Nk3/bH5nZ2dmZkaafmpqamVlhfQe9S8YlAA+PbyLBgYGOi2knZycPDw8PD4+nqpp f38fm8/1vpNEjL9X6b2YPek9yhj8d999d+nSpWvXrl25cuX11183Ni8pfacvJUPU4uKidFfTaeUx Nt9C6+vrs7Ozm5ubfbL5enrvxY2EUcGSIWFiYkLMXrrc+Ph4O5mgjOQytkunNUO6RKPmtsjdh6Wx 2Ly0nZj3/Py8REd9svl6ei8DPuk9Opn6SQ4/PDzcZg4oI7m58bl0XZONSnddqUkGMBn2sfnW47w0 ljScJEV9tXlzjTk/DxlJumfGgKOjI+lv7Z9sZ4x8syYzUJnuaqaiZPTC5ltITF0ipf7l86T3qInB v6jtjb93716nOXx6PJfHjgT2Hti8Gd4lUqrPdorvNPP2/Zv/JL2PXNVqVa5+PcuTcb79jG+/JjPU 1yNTifZLD+m9sXlpPmkvyYuKd5Ok93Fqrqbcvy7BvInep6amzMSzWaUzGT4235bE2sta1SS9x+Dz Badi9tJp0zNQ7oi9tKT36PeELpIL7YfNi78scQqE9B6Dz5eWrq+vY/P5m0/SofT6fPEivQ9VR0dH /dhnKcn8yfUmbN4zkd4HmbvFdk2xedJ7DD4uJ47Nk97HG7VJSB9h1IbNk97HqHSZHTaPSO8xeGwe kd6HIlN1E3OAhs2T3kdn8JE3AjZPeh+La8bgsfkea3d3l/TeWYMnBcPm+6KjoyP6FgaPzRNDotLE /Uuw+YK0urpKeu+CwZNtYfNFp/fcDBuDx+ajS+9lzE9H/gz+BUiC+TjrarF5h9J7Y+ry8ebNmzRL vw2exAqbdyK9Nzc5y3cvFITBY/O+pvdjY2ODg4PtH5aO2hd1tdi8i+m92LwM9efPn19bW6NNem7w tAM274QWFxcfPXok4/xnn30m1m7udjg8PLy3t0fjdC8zaVKtVmkKbN6hEf7777+/ePFi8rJGRkYI RLs3eMrssHl3LX96ejpzP/M2b3WKMHhsPhzLv3v3Ls2SQ6audmtri6bA5r2x/A8//NCY/Q8//ECb dGrwlNlh8/5pd3f31q1bAwMDr7322vLyMg2CwWPzUWh7e/vTTz+V0f6XX36hNVrK1NWaAieEzXus X3/99f79+4xdLbW6usqsJzYfrObm5kZHR6/VNDY2trS0FE/0fvv27ZGREfnH5aNE8tQyYPPh67PP PktOKIZafTHvwcHBzD8+PDwsSRC9ApsPVtVqNWmkgYGBjY2NsP/369evN/zfJdKhY2DzwWp8fDw5 RRL0tv86kvp2s4LdTbnLQU05fuvkIF9X8P4Om49Xksee1u8luW3/de7cuZO7cEVijdxH95sNRfUd xO1rd3c3OV3sosHmg9Xo6GhPbL6b/eRmGTz3UJ9vo1tzm2cPMjYfrO7evXtav3/y5EnA/7i4p9Ni +6GhIZblsflgtbe3Nzw8HGe/F6fW0Obv3btHx8DmQ9ba2trIyEi601++fDmSZerp6emBgYH6Py4j /61btyjFwebDlwzpksHerkkeRNXpt7e3zUEj8pHpemweIYTNI4SweYQQNo8QNo8QwuYRQtg86rt2 dnbqi9IzMzM0SFqTk5OHh4fHx8dTNe3v7zf/eflhaUNpSfnFxcVFGhCbd1Tz8/MrKyti/Nh8RtIg YrrGLcrHNs14bGxsc3OT1sPmXZEMVjIKiZ2n+6V0bnleBjQaRxpndnbWDOniCs0uenlQ/xn57uQJ pRsTm8fm3ZIMVtKPxbzF7OtGLg+kp7aMXWNoHHNOhhh2PfFZqWl9fb3NOAibx+ZdTOBNMC/5p3nG dHdJWWkcaZzNmoxDNFG9SXzES2Lz2LyvaaqEo+axDF/msXiB+pORN056PJfH6cAem8fm/ctXRTK8 y/BVj+Rl+DJewAz4kTeOGepNBGTCn/anNk04IDYfeUti8w7JpPEmX+10+IqncSTHMQO1WaXjJExs 3vvRTHp2O6vNcebzpnHq4zzC5hFC2LyHknGM2L5JKLS+vk47YPOhdWtJUynCaShJ5lnCwOYRQtg8 QgibRwhh8whh8wghbB4hhM0jhLB5hBA2jxDC5hFC2DxCCJtHCGHzCCFsHiGEzSOEsHmEEDaPEDaP EMLmEULYPEIIm0cIYfMIIVdt/tVE9f8B24LdFuhSDAB= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0034_image086.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhswCoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCy AKcAhwAAAAAAAAoKCgEBAQQEBAgICAkJCRoaGgUFBRQUFBkZGRISEhsbGx4eHhERESMjIyEhISIi IiwsLD4+PicnJzQ0NDExMTc3Nzw8PCAgIC0tLSUlJTIyMjk5OTAwMD8/PyYmJkxMTFhYWFJSUkpK SllZWUNDQ0VFRVZWVldXV1BQUFNTU1VVVU9PT11dXUJCQk1NTVFRUUhISEZGRklJSUdHR2BgYGNj Y3JycmFhYWVlZXV1dXx8fGJiYnNzc2xsbHd3d3t7e3Z2dnl5eW9vb2pqam5ubnh4eH19fX5+fmRk ZGlpaWtra2dnZ5ubm52dnZKSko2NjYiIiJGRkZiYmJ+fn46OjpycnJSUlJqamomJiZ6enoGBgYSE hJmZmYuLi5WVlZOTk5aWlpeXl4ODg4eHh4+Pj4aGhoqKipCQkIKCgoCAgIWFhaysrLq6urS0tKCg oLa2trGxsbm5ubOzs7W1tb6+vq2traSkpKKiory8vLe3t66urqmpqb29vaqqqqurq7+/v6GhoaOj o6enp7KysqioqK+vr7CwsLu7u6ampqWlpbi4uMbGxsXFxcfHx9bW1tjY2MjIyNnZ2cPDw9fX19HR 0d3d3dzc3MLCws3NzcHBwdPT09DQ0Nra2sDAwNvb29/f38rKys7Ozs/Pz8zMzMTExMnJyd7e3tXV 1cvLy9LS0tTU1P7+/uPj4/j4+Pn5+eTk5PT09PHx8fX19eXl5e7u7unp6f39/fPz8+rq6ujo6PDw 8Pz8/Ozs7Ovr6+Dg4Pf39+Hh4ebm5vv7+/Ly8uLi4ufn5/r6+u3t7e/v7/b29v///wECAwECAwEC AwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwEC AwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwEC AwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwj/AFsJHEiwoMGDCBMqXMiwocOHECNKnEix osWLGDNq3Mixo8ePIEOKHEmypMmTKFOqXMmypcuXMGPKnEmzps2bOHNKZCaTp86fB5m5egUTViyf QJO2YtZIFtKVzGA5YvZUKU5mj9pQpQrVlZNXsyBVXTrWKlRatWwwewLFVtmRzG7dwBUpCteBuKRI emsWJbMQbnLpmjKJb0hmu0TsovIGjqutVOPIMdy3JLMqlJhVmkOL8kdmvKz0wjHCkq8rWKbQYRYn jufKcKnmyLHrtcetci5lwQWZmRUtr2zDFrn1JeSCxYfHTO73rnKdVC1hEo6R6q9Gzp/bBP0gQAAS ZQ3z/81OkBkO7wIKa7/JrIR373WqMsuECyEzN/UNMqOlaSwzYO8FYAJ568HEzAkBbiEfF7z45wsV wfgnzBT+QRIgBAQWyNJWdgRIYIZkvZUhVRG8dwd1GoK01SZUDXNFFSDexgweTnAiVIwpEkdVFwO4 FSKKF/XWiRc45tjRVl94BwuQh9UCRi9MGhkRYjq812BNzBAjRTFRSukQM8bkIUEAnnSp4xOVmOll QlRtogcKe6ipYx1vFLkmRMy8QoVYkchJEjOf8GHnnQwxg0kYwS2lFDOgiKEooRNR1Ycfg2I5SxhX QoonL2CE4ueGsODRp6YNUSVJHlBqR9Uf2JGqEFWAzP9R6U9UBXLip1B1yUwtWdSCa0+h2PXarxkx I8ooQFJFiSCzmhXXGBEuxIwTxF5EzCRk4clMGKQ021eeXvjKpjFHeaviJDvAUkydX9ZixSzVbsfM IDbyhtwvjvDATA/ExDslMVhQNUG0rzJTx62uUmXHG8c8IR8ZlPrwCzD+PsRMKE8clUK/rxLzRH8V XxULIQTAOxBVKlBaQCmmhPxlcL1Q0DKboFDhlKvlFbOCAQEc4FyW855CQprLtdJLMAQjx0whrrmc E1WDIBAACz8zgwzQWIaHSxTGOE0rVVoEUIZ8jz4NGYteJ0UVLBVo9SNQzOjRwg+1mQspVcb0y8cJ QNj/fdKMAZqMs7ZBvJeA35ZZEKAhaVdGlQIBIvu0CwFSOviUFwSY6FW4YOCdEI3DxowtJQbwR+iR Hnf5TqrDfdTqkYqBukXMDPE67BbfcsjsFTEDxQu8O1vILcFHmkkAlhQPdytEOntLABkgfrcndii/ Uy7eUWH9031w6ewrBaiwgPe4s/kKs98Ss4LVwmy/3bHuR4TLktLfyQwcS4rODLvl2zfL6cqZ1836 px83XCJ+kZKFKBDYE+0xkHUE1M8u+Pec+hmJGYBIxgN38gpEbLAlvvvgTgQRwZOhIhAinJIpfJFC vzjBXgWyYAyZYZccyfA5xEBGKjrRwimpon3F6o0Q/4dIxCESRxYnKAQsdNFDi/HCgxTpjS86gYg8 /IEPdaADHeLAB0B48YtebAMh4lCHLNLhDX/4wyAMkQhOMJGIxcKeBhhww+UQgjqQgUQe7qAIPJzi GEUMZCCDUYtSdLENdeDDIOTgiVfwpnV44oR3xGVDi0VlE2MgRJp6cyQ4gqIOgHhDHt4QCvrNihmC CAARmpi6gglFEIMgXh1ZVxxL8IEOXihFLiAZFCEEYJY9aUR+9MMMXIwCD59gzkwgsws+HAIOw7ja eGAAB1bupBOZkI/V9ECFTaptK6YoBCGEka3yMKMI1rzeVLhCFV4A4g9dS6c5mbGJRTDiF+ykCjI2 5/8lZkRiDG6wTiEQ4RZ5BoUqymDEEx6TCi8wApg0ucx7YsCHRCwDoi7ZiiqM8B4ZYNRAzGhA4D66 HAcEaBUG/RIzIKA5n5A0V8zYQIBmZkNmzAIRUyiAd7jg0mml1D6JgEEgiPAeIuihaRqiSh0I0aBZ UMJTJ/MDB34alE4cQSgpgISnmDEJJ+BTVcw4RRa2GqKT7YIUHaCqfpDQBmAkwVc9pcIjXkqcWYwB ZGyaQio8wDGwfoAXytBB0sgiCUKkylnM2IMhrvYqUUQCFioA5HqYoQwlUAUEyvCPLq7go0Ul4wmp wBEzVLGEXtCCCdRSlZ6A8IYtdM0+vTDDY9R2iir/9FVanJxsbu3DDEOMCjqAQFsJS8WMK6Aihcw4 w2yHq1IxZJY9aMgUc1U6tgeiknjTnZJvGMgMOiQvuzupRHx6cgtFqDWiV+jMcraQP/DuJBiMM5Au AureKBbiqxlVxXfruxNQLNA4mWAhfyPVvIzqob0DxpMcemEcP/AzwV9yBH43dODzbmcUw1AeM0yh QQjjaQ6DVQkzOkE0D3+pwCCEBA9NXCpejDejttCDhSOaCVBsz6csLpSCliMH9ebYPpygqXEqcYoZ LwcOZcvoLWT846A0YsU9iW+Tzam9iMJoyuURDXchYSMsL+UUU8FSMl7cZMpmYYPMWEacpkyVNIiQ /xmTYfMVOsye1P6YGX7Yy9PQl2OuAqKFzDgEY03MjF9UGTqSELCHqSIsWiXayJZRw2GhgwdI/2kL TFQbnxMMKBYt6gqWPswtrryoE3G6F1ZIZ57WPOC17NIqNnVNqwOBUmclQ9b1ZcYxpAzrYyQz19ua 9KIiUaZcH+KAjjNFZ7P7n92JLhOCY7YXYPgtaIdaI8z4A1SfHW2L9Q5ut+C14zZBPovRQiBGPNkQ Xw2d6gZQFJK12CqQxQw74AERdzgGF2yMbktIYA586AEzArGFX2TmaYTIdACFITmLoZMZa5gMM2bA DI+6dBYhoMoCm5DhINA1iqSg4HAK7ewvxQIMzP/wxPrwZotEIGVpNMiCjZdxq01YDku8APVkg/FQ iz3C5UeoNC8MUU2esJMGw4gPxYwOCTZYd1sftwyFLEaKRRjsDFSpwYqZAYmLMuMDbXrtUiJh6ohi odsV7IR6viRwRgliDrVBdxZQSIchiPILL0/CspdDBYqliCpT/9IiNNg6zXBpt2mWXUQVwYprJ5aS peoWb9kE5Z48ofI2XMMpv73MNvC7n7II2LULtogME+o/oB59UJZhhr2vyVBUQHA/mbEKN6s+KK/I ZdRF3ItBVO/2vD3FEzK8+z8ZSxCuxxlV6FCFVDwygFSJBBW6BXziGqsPjDBGWReVJU7goWXV1+7l LB5xhz5EgoW87EmL9ICHUhQfsdGhRB7mwAljmFKZzeFKKDKBh03gM/zYRhXBMAmqYAdj0EasoAv9 km4bMUS6kAqasAiGoAnoB4AyshWwgAqpIAp7UAVyYAqkYAmVsAsRIkgmCBm4IAvC0AmdYAqEAAiq sArl8n6nJ0Sy4AqREAmkQAmFsAiEwAefYAeloAqqwIJGeIQsSAqiUAqOEAh0sAiK8AaZwAmTIAwN kn5e5kpDhAzBkAy2cAuoEApiOIZkiAq3YAuzsIAMmIUccYJCxIZwGIdyOId0WId2eId4mId66BAB AQA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0021.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

27

Uniform All-to-All Traffic: Summary

•<= /span>a: cost for each unreachable destination

•c: cost per unit flow

•a/c < n-1: no stabilizable MSD

•<= /span>a/c =3D n-1: directed cycle is only sta= blizable MSD

•<= /span>a/c ≥ 2n-3: all bi-directional trees= are stabilizable = ;

•<= /span>a/c ≥ 2n2-2n: All MSDs are stabilizabl= e; no other stabilizable graphs

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0020.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

28

Social Welfare properties

•

•Complete graph: n(n-1)c

–Best connected graph&#= 13;

•Bidirectional Star: 2(n-1)2c

–Best connected equilibrium

•Cycle: n2 (n-1)c/2

–Worst connected equilibrium

•Conclusion: Ratio Between worst and b= est is linear in n

•

=
------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0020_image087.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjA4oJbAzMAJYm2sZgQxmHOZGRiYGGTAsqxAzMkEYzExMkJZjEz///8H s/QYJaBi3HB1PEwJzAfUhIAsNTZ+BimG/yDFDAIg24CsdUDcoMbAwAe0hxuqhofBN7EkI6SyIJWB 4QHY7t9MrP8eg90wAWQpEwsTg0BwZW5Sfg4Dg6QEV9yMJ0IMN+Z/Ln8IxAoKX8sDxNNqWIAKdYGq OYC0Edc8RmWwezUqCZnHKc51ELd5jAwg+gOSuQeZQEZoVhLhzvgfj3G7E2IuI9zcq+xEu/cQbnMx 3VvMSbR7EyJIcG+lINHuPRxBgnvFhYl2byIp4XuWh2j3HiElfDXVkN174C8DbvcmZTwl1r0/Gdm4 QUY8rYTxF7FA+BB7Gv4x4Hb/Udz2oLt/AeN2cHhrV8L42lwgvi2cX8kM4UPsVfgPsxckCrI3JDM3 tVjBL7VcISg/NzGPSP/xM68D+y8Tag8DE6cgMp+f2YsVVT6VHcJH9z9p7sD0/1JVZHsWMF4UAfET 4fynYHe5V3JC+c18IBPScvLLYSrseUEqknNgfEcOsA44P4UNxHeG8/sZUeUdGED84BwsMUtBCC9g DAf7TCEH5vJqJbDLi/JzYSrUlcAqirig/K1yoBI8Lz8ltRhuSrQcWE0+jL9QFsRPyeeB8q+KgXSX 5iXn5+WlJpekwsNNFKROGa6vWxTVnIe8ED4XtBbgAtcUYE9D6wABBnYwbw+4bmFkYlIKriwuSc1l qAH5mgGoQ5GhC6wBRLQ8F2JAj2NmsH4Am3wH7vAGAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0020_image088.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhtAEnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMABACv AR8AhAAAAAAAAAUFCwsICAsLDQgFBQ0ICAUFCAsFBQgIDQ0IBQ0LCwAABQAFCAUAAAUIDQgFAAUI CwsIBQsFAAUABQUFBQgFCAAFCwgICwsLCwAFBQsICwUFAAsIDQgICAgFCwX/ICCOJLkIZSoOhOq+ cCwD58zOuFznfE+jsptvSCwaj8ik0tbKLQrNmOEQXSqf1dc0azVBu0TsbAsum8/oNI+MQyRyBiBP Eajb73fGm+iGy2V0eIJ1eiV9ajOHY3+IjY6PkIs4cT2KOYENXCIGDg9ElDyWMZiaAJyeI6A+CxB2 EUiqbXtWYgavkZASDKU+uryjhL9JooEBDzUStyUTdplCyUOkLgqoKcwBetQl0NbNBM/KM9Iq2iPc PQsOEQsUFdVF5yTXAc5N8VdA5bhHCxbCAMx2JQn4j1wmTuGuQMgEIJ4CgQCNPZklgg5DUw4upKIS rc7FEgswpKCjkQaEQiMm/5aw2IRTSVMcL3nUFDJlAYo5JpQUY0QlCZabMm4suOaWqH1D2MTwpYSp D52OlE5QNpEdRQkBEkqoZoACTpn0CmINtyCmCKskxm7j6rXHuBdo3aJUGqatuaxrU9m1SZScp359 kbqY8BHGw8CGIfaA2qjrrAmKWXSN4jKFgVnp3rmdKUWoCUaTU3kmcTllJx9vVYRO2cqYClaE3igI V+xYq4sICLBSthrjy1SYT3v5xSkr4Sbz7OxKF0Ajs0ysLhSvFghlQ1dnIUh34Dr69LvYolR/g7VO yfIQr1VQbHK7axHl8Y5QDxF9k0AXhBQ3D7AB1vPYiUBYBtw5h81V4Z0lHP8N3L1z2HzWuZCZEdX9 AtlXIyl2YQwTohbMCw8q+MpULzAGgCKQtRAaUw+9oUqIAEX42oJnfeGCLuTJN0JuplClHXwNEBiA BlQc1xB0J7UgAUMkMUckAQNy96SRJLLC0JK6JbkBlgK+YiWU0DmgmJNFXslkcwKGKVCVC+nGkQIf RWfSkAJgyWWTre3yEAe2/QaAAi91OB+aFUGUzkfFGLpgcnb4OdKHr7UJiKKIKteEoIzyRw6kGUZR ZQdwQXALO/Yo6oljT7RVWqGXOlAppILWWEqLm+xFw5vVyHlkC0Zi2WGLp5hTSK8MEUvAanQcIxyt XCIbwAF2OTWfmccuiKP/Y/Dt4uwDwQIgRHvCtmTtsAx1yOV8udIIH6EhpuOnrgpqlpStII2WWKvv /miavHDQ+xNEvWlhF6Dx6uWiVwZ40Na37doL7r4CDhKnqCPAmKlAunLJGJYwFjpLsgCdV6zIBBTj SsdAtmByHevdx17IKdNakTEhHrYyXtckBO+5Mv/pGpfmxrnXhKsKKNBqh1YRa6xETMCvaY6qRkGr hS2tLg9Ow7CaBFF3Ch8qMDKVTgQYZKaPKVMrWDWNTPO0kqH6VvyXjQ9rTHLPM3N12sYjx1zYnzLu +mdhTqHMd8nvYfRA4Xr+nV2C2b3Ec+LBAi3cuYNHMWE8Yu+1YcXsYRux/yBdm5OQCimaIBJInkfY segRkX7j6azvYSIMRk60AQHnIqTgAQmMzUhcMVL0Or1upyV54vC9scN8JMO8q++bJFAZq9LbnTLs QfFGHkPcgwx4FodfP774h3FPA6iKsyb5ReY/aDkqmMeDLTOoUM9KutYZORSFpSONmFpiFzHszzT9 KwxdLhHA7NBPIJgzgTo2cYAMfOBYqhqNuxiEsS8cUEEJrMICk2eOYlWAAhhYnQh4ZItlHIQ7uzhc 8VbIq+5QLHt9E1zqGuKJz/EISxuIkT0iMMDrREiG+DOJl4qIFT3scCto+eDDBBexv9xwfimrUQIk sIct1GAe77gHozQzG/8jLDBU3pjdMvBARtrJ4Iwq4AZsdGSZgUFuPKqTVRwTMsaVnI6ECqrDA+gw Jn/8STPF8U8MzVOeYtmhGvFBxTUu0MjWUJIz81AGGIPynkwyiGVHZCRnImkaUNoOOwvYAHcSx5wD XUMxpLwOPQawygdco1zcUUYZ38gIGRzFCWnjR9xikQgMcSiYvORBBIsAL2L60piCiaY0pykLHHDR Cb10wk20Bs28mKObIMkmh7aphauAkzVPG8JW0nLOlIiTmvCMJzyfpwNDJgIx8kjnCtuZPMC0AZ9Z g4El/BmqxTWQB/20py/xKc+GOtQMPPLDDAKqTjdCqCDOdCbq9KlG3L2TTKPyIJQSMvrOfD70pCiF BEXhebNBhEUcdExDSyXGUDDQwaIpzalOd9qImQ7ioLjwqex4StSiGvWoSE2qUpfK1KY69alQjapU p0rVqlr1qlhNAiB5utWsevWrYA2rWMdK1qXCy6hnLata17rUdSbVrWyNq1y5Sje01nWueM1rPEG6 U77q9a+AdcRNkzrYwBr2qyEAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

29

Robustness

•A notion of robustness - how sensitive results are to parameters. •Measure as largest spread of accept/reject bids: = 226;For hierarchical graphs – most robust is a layered connection.
•

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0019_image089.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBgAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAB AAEAgAAAAAECAwICRAEAOw== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0019_image090.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhoQAMAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACe AAoAgAAAAAAAAAJVRB6gy+0Po5y02oszQrn7D4YitZXjiaaqVybta67yTE9bB+cJejxcDWzsGD2g DmYrLmLB4K/JOraWTOisauXdFNKu9wuWZldP7nYsK6NPQ6FyrWoXAAA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0019_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhwgBgAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADA AF4AgAAAAAAAAAL/hI+pEcfQlJy02ouz3rZF+HGi14nmiabqsrbuC8fyFr71jOf6ft78D1z5gq0h 8RgzYpREJvIJLUanVEfVqcFCtdUUN/HtZkgfkrgbPlceJWr68lZLs/L5uO7FU+J6VpMP0WeiBahW aAV0KLSjiNR4BSdIJ6n3uEYpYYnJuNnponmJA5rouVhqMOo4kdp0iuoKa4fHwJZpG/sK+0jLagPT 61fHWxuci7sKLDsSwku5i9x8nDkMEokoDUb9+4kyTLzZWNZMiw0y/r10rRuNgM5tuqfdnpwT513u IC8TQV/EPqXIg74f/W7FI2ew1D1Vgc4s7PPlXkGI5tyFqjQQ0sR5/whd3Xi4Ct8SbYU2TvsnyYyX jhwtQlrAMh9KGtIkziw2wh8zaiBxuRzjLajQoUSLGj3KL2jIbjUzWuuhU9xQkYd6gvv4TynUlyp+ XhxULyZMqxBNimzYUqyxszm3ptR6xSzVQWTBsFXHQe4+uKi8Lrvbyu1JvuX46HXEruRhbIZpILxJ U0hjwXsdZlN7R7JfjGOVAIq4E3Mip22Ydu1Y90g0yEBPI30NOzbSvrJr2y4Tl/WerprTLqadpKro lIO/gs3MturK31uY8+5GeingIIcJT1973bfAMAHRRElGdnNy7B5lDseL/Hn23a51+6pJ/u3qwOt5 YElNP5bzwefRY6NibpZU/QFUWDuqRddWfer5B5RLC+03SRIMRVWLVRC64R1d1uG0jUL6IXjMhXkk lAWICh5Hyi8DxifhiXmxZ1+KI8aooIgw4sOEjTXWFyBa6YxXGmA5EsjVDAAGQkZ2hLh4YkRMyjGK jk9ukeCURTJmpRhSZvnjlShy+SWRlIGpGplcarKlklpGZqY/ERrZQZr6damDSgy2yU0NdlLnI54x FlIAADs= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0019_image092.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBQ4G5gZuQEsTaEMTIAGcy6TAwMTAwyYFlWIOZkgrGYGBmhLEam//// g1l6jBJQMW64Oh6mBmYFbiEgS42Nn0GK4T9IMYMAkH8AyFoHxA+4gDqZgXqgangYfBNLMkIqC1IZ GD6A7f7NxPrvMdgNE0CWMrEwMQgEV+Ym5ecwMAhxcQX9eCzEcGP+5/KHQKyg8LX8olTaehagQl2g ag4gbcQ1j9GEBaRVo5KQeYvEuJbgNo+RAUR/QDL3EivICM1KItwZjM+dEHMZ4eY+5SDavUtJcW8z F7J7D/xlwO3ekIynxLr3J6MbA8iIp1BzFf4z4HbvMtzmoruXn3kD2NxzGOaCREHmhmTmphYr+KWW KwTl5ybmEelefmZ7sAnulTC+GQMoyWZmQfgMTEYcqPxGZggf4o6Gf+S5A91/CxgDOcHuyILx1dhB /Fw4fwELqrwUE4jvi+EOBorCYwFjDhvICN0sLmgu5ALnVLCx0DwowMAO5u0B521GJial4MriktRc hvUgcxmAOhQZusAaQETLcyEGdD8zg/UDAKiK7z5wBAAA ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0019_image093.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhnwAyAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABQCZ ACoAhAAAAAAAAAUICwsIBQgIDQsFAA0ICAUIDQ0IBQAFCAsLDQ0LCwgFAAAABQUAAAUFCAgFBQUA BQAFCwsFBQgFCAUFAAUFBQsICAUFCwAFBQsLCwECAwECAwECAwECAwECAwX/ICCOZGmeaKqehrCW A/HONOvWsVkEfO//vkNtiEIkFMMFQ0hsFo/JZUnJayBVBkeA6SQaHtckRNYtf8O1xXiqDUBViwi5 TFNyiUY0vS515ktZPBIvE3N7K39OCw53hy+JTYuNAIEBNykGhiNUbnoiizxvKEqDJ5w8BwsUaAWi jnAMpSanW6qsriIIPZdNWVYnO78rWZNUssYlCA2aryyMswwBx9GyucsnAz2TNLrXyTy8KQPeI76a doAO4c0m45rmU33l6ig7AeRDExX4lBb7zMCEfXLAT0QOElmqsdMhEMCiggAOzlNIwl7DGQseZLuj 5oIDXKYYNNyxTsQEPYtA/wJDFVFark4plIy0hOIkG5UOo93zpAKBAF28BhzIVnLWxzC+eI4iqNSE ATkFBBSwgkDCuKYpkTJNs3VpqKYmCumS5VMmQKdHR2SjCAsitgRCZV7AAGDqWUppDbpMI/Iu3nt+ SdhK+AlM1hlZRJEsYa8KGrM0CmSgm3LVYRSJwyyu6KMh5J5barRweFSNDKA0Mn+Ktm2z4L5/q5xz AAaArgcyshQVoTpnaB0047kduBubDJkKhIqwW6dr3eCCnW8SiaQS4G831hocTlqg603SV198zTbm qpwN5g7ECU3gWLRsL6+YigQ5erD2X1IkbJR9K7BO0bXcTi+t85QCTxnC3P9qv6nVYHTlxVMKf4tM GAGCclREDhWNbGSKAxFeFcUl7jBYXDv4gMJFfumcyNsztv0GVG3ipKjFitQ5U5QygTHWwy8++faj gg1owIArxLTzg1s8ziBiXcJk88tURiIJIwnZdHZWk2hts1A5dAVJHh3/sWNAmOGQQiZIi7gYUY9O ClGICcoAGJM8ryg3ZzLj8VFMLBhBYOcLpsXhCTp+sKfIGIZC4+UjIJUJ6aDDgHEmZjSKAecQZ1zK QqZprAFDn8BFOMRGymEm4KmPloHqo56ySicQtP5gKhGm9eSmWrsu6peYNAxgYBu11torHA+o9+Wy GSm7LGfFFtsqX6Q+SweCi9Zmq+223Hbr7bfghivuuOTOA9gFlJarLh0HJqhCiWquK6+6dZaz6bz4 1kDlkVdkSZMSx+YrsGho5hKOu88ROPDCTuhJhr80HajWrQxXPAujFxp0TobLTWvxx7xZumqsI5TZ KMgoo/AqlruU3IOiKYOca8w0d9HsqjXnTG26OuscAgA7 ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

30

Ongoing work

•Undirected links <= /span>

–Not clear who’s paying who anymore

–Only trees can be stab= le

–Convergent dynamics vi= a a potential function

–Bargaining games and sub-game perfect equilibria

–Massive simulations &#= 13;

–Efficiency loss

–Modeling flaw: the hub problem

•<= /span>

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0037.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

23/6/05

31

Potentially Interesting

•User response

•Fixed link cost – cost sharing&#= 13;

•Routing as part of the strategy

•Delay for QoS traffic&= #13;

•More complicated contracts =

•Realistic applications

•<= /span>

•And did we say dynamics?

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game

A Contract-Based Model fo= r = Directed Network Formation

Shie Mannor

Joint work with Ramesh Johari and John N. Tsitsikl= is

------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/master01.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
‹header›

‹date/time›=

Click to edit Master text styles

Second level

Third level

Fourth level

Fifth level

‹footer›

‹#›
------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/master03_stylesheet.css Content-Transfer-Encoding: base64 Content-Type: text/css Ym9keQ0KCXt3aWR0aDo1MzRweDsNCgloZWlnaHQ6NDAwcHg7fQ0KLlRCDQoJe21zby1zcGVjaWFs LWZvcm1hdDpub2J1bGxldFwyMDIyO30NCi5UDQoJe3RleHQtYWxpZ246Y2VudGVyOw0KCWZvbnQt ZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCWNvbG9yOmJsYWNr Ow0KCW1zby1jb2xvci1pbmRleDozOw0KCWZvbnQtc2l6ZToyMDklOw0KCW1zby1jaGFyLXdyYXA6 MTsNCgltc28ta2luc29rdS1vdmVyZmxvdzoxO30NCi5CQg0KCXttc28tc3BlY2lhbC1mb3JtYXQ6 YnVsbGV0XDIwMjI7fQ0KLkINCgl7dGV4dC1hbGlnbjpsZWZ0Ow0KCWZvbnQtZmFtaWx5OkFyaWFs Ow0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCWNvbG9yOmJsYWNrOw0KCW1zby1jb2xv ci1pbmRleDoxOw0KCWZvbnQtc2l6ZToxNTIlOw0KCW1zby1jaGFyLXdyYXA6MTsNCgltc28ta2lu c29rdS1vdmVyZmxvdzoxO30NCi5CMUINCgl7bXNvLXNwZWNpYWwtZm9ybWF0OmJ1bGxldFwyMDEz O30NCi5CMQ0KCXt0ZXh0LWFsaWduOmxlZnQ7DQoJZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJp ZGktZm9udC1mYW1pbHk6QXJpYWw7DQoJY29sb3I6YmxhY2s7DQoJbXNvLWNvbG9yLWluZGV4OjE7 DQoJZm9udC1zaXplOjEzMyU7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJm bG93OjE7fQ0KLkIyQg0KCXttc28tc3BlY2lhbC1mb3JtYXQ6YnVsbGV0XDIwMjI7fQ0KLkIyDQoJ e3RleHQtYWxpZ246bGVmdDsNCglmb250LWZhbWlseTpBcmlhbDsNCgltc28tYmlkaS1mb250LWZh bWlseTpBcmlhbDsNCgljb2xvcjpibGFjazsNCgltc28tY29sb3ItaW5kZXg6MTsNCglmb250LXNp emU6MTE0JTsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQou QjNCDQoJe21zby1zcGVjaWFsLWZvcm1hdDpidWxsZXRcMjAxMzt9DQouQjMNCgl7dGV4dC1hbGln bjpsZWZ0Ow0KCWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFs Ow0KCWNvbG9yOmJsYWNrOw0KCW1zby1jb2xvci1pbmRleDoxOw0KCWZvbnQtc2l6ZTo5NSU7DQoJ bXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0KLkI0Qg0KCXttc28t c3BlY2lhbC1mb3JtYXQ6YnVsbGV0XDAwQkI7fQ0KLkI0DQoJe3RleHQtYWxpZ246bGVmdDsNCglm b250LWZhbWlseTpBcmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgljb2xvcjpi bGFjazsNCgltc28tY29sb3ItaW5kZXg6MTsNCglmb250LXNpemU6OTUlOw0KCW1zby1jaGFyLXdy YXA6MTsNCgltc28ta2luc29rdS1vdmVyZmxvdzoxO30NCi5OQg0KCXttc28tc3BlY2lhbC1mb3Jt YXQ6bm9idWxsZXRcMjAyMjt9DQouTg0KCXt0ZXh0LWFsaWduOmxlZnQ7DQoJZm9udC1mYW1pbHk6 QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1pbHk6QXJpYWw7DQoJY29sb3I6YmxhY2s7DQoJbXNv LWNvbG9yLWluZGV4OjE7DQoJZm9udC1zaXplOjU3JTsNCgltc28tY2hhci13cmFwOjE7DQoJbXNv LWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouTjFCDQoJe21zby1zcGVjaWFsLWZvcm1hdDpub2J1bGxl dFwyMDIyO30NCi5OMQ0KCXt0ZXh0LWFsaWduOmxlZnQ7DQoJZm9udC1mYW1pbHk6QXJpYWw7DQoJ bXNvLWJpZGktZm9udC1mYW1pbHk6QXJpYWw7DQoJY29sb3I6YmxhY2s7DQoJbXNvLWNvbG9yLWlu ZGV4OjE7DQoJZm9udC1zaXplOjU3JTsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Ut b3ZlcmZsb3c6MTt9DQouTjJCDQoJe21zby1zcGVjaWFsLWZvcm1hdDpub2J1bGxldFwyMDIyO30N Ci5OMg0KCXt0ZXh0LWFsaWduOmxlZnQ7DQoJZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGkt Zm9udC1mYW1pbHk6QXJpYWw7DQoJY29sb3I6YmxhY2s7DQoJbXNvLWNvbG9yLWluZGV4OjE7DQoJ Zm9udC1zaXplOjU3JTsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6 MTt9DQouTjNCDQoJe21zby1zcGVjaWFsLWZvcm1hdDpub2J1bGxldFwyMDIyO30NCi5OMw0KCXt0 ZXh0LWFsaWduOmxlZnQ7DQoJZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1p bHk6QXJpYWw7DQoJY29sb3I6YmxhY2s7DQoJbXNvLWNvbG9yLWluZGV4OjE7DQoJZm9udC1zaXpl OjU3JTsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouTjRO DQoJe21zby1zcGVjaWFsLWZvcm1hdDpub2J1bGxldFwyMDIyO30NCi5ONA0KCXt0ZXh0LWFsaWdu OmxlZnQ7DQoJZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1pbHk6QXJpYWw7 DQoJY29sb3I6YmxhY2s7DQoJbXNvLWNvbG9yLWluZGV4OjE7DQoJZm9udC1zaXplOjU3JTsNCglt c28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouT0INCgl7bXNvLXNw ZWNpYWwtZm9ybWF0Om5vYnVsbGV0XDIwMjI7fQ0KLk8NCgl7dGV4dC1hbGlnbjpsZWZ0Ow0KCWZv bnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCWNvbG9yOmJs YWNrOw0KCW1zby1jb2xvci1pbmRleDoxOw0KCWZvbnQtc2l6ZTo4NSU7DQoJbXNvLWNoYXItd3Jh cDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0KLk8xDQoJe2ZvbnQtZmFtaWx5OkFyaWFs Ow0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1jaGFyLXdyYXA6MTsNCgltc28t a2luc29rdS1vdmVyZmxvdzoxO30NCi5PMg0KCXtmb250LWZhbWlseTpBcmlhbDsNCgltc28tYmlk aS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3Zl cmZsb3c6MTt9DQouTzMNCgl7Zm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1p bHk6QXJpYWw7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0K Lk80DQoJe2ZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0K CW1zby1jaGFyLXdyYXA6MTsNCgltc28ta2luc29rdS1vdmVyZmxvdzoxO30NCi5DQkINCgl7bXNv LXNwZWNpYWwtZm9ybWF0Om5vYnVsbGV0XDIwMjI7fQ0KLkNCDQoJe3RleHQtYWxpZ246Y2VudGVy Ow0KCWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCWNv bG9yOmJsYWNrOw0KCW1zby1jb2xvci1pbmRleDoxOw0KCWZvbnQtc2l6ZToxNTIlOw0KCW1zby1j aGFyLXdyYXA6MTsNCgltc28ta2luc29rdS1vdmVyZmxvdzoxO30NCi5DQjENCgl7Zm9udC1mYW1p bHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWNoYXItd3JhcDox Ow0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0KLkNCMg0KCXtmb250LWZhbWlseTpBcmlhbDsN Cgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtp bnNva3Utb3ZlcmZsb3c6MTt9DQouQ0IzDQoJe2ZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRp LWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1jaGFyLXdyYXA6MTsNCgltc28ta2luc29rdS1vdmVy ZmxvdzoxO30NCi5DQjQNCgl7Zm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1p bHk6QXJpYWw7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0K LkNUQg0KCXttc28tc3BlY2lhbC1mb3JtYXQ6bm9idWxsZXRcMjAyMjt9DQouQ1QNCgl7dGV4dC1h bGlnbjpjZW50ZXI7DQoJZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1pbHk6 QXJpYWw7DQoJY29sb3I6YmxhY2s7DQoJbXNvLWNvbG9yLWluZGV4OjM7DQoJZm9udC1zaXplOjIw OSU7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0KLkhCDQoJ e2ZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1j aGFyLXdyYXA6MTsNCgltc28ta2luc29rdS1vdmVyZmxvdzoxO30NCi5IQjENCgl7Zm9udC1mYW1p bHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWNoYXItd3JhcDox Ow0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0KLkhCMg0KCXtmb250LWZhbWlseTpBcmlhbDsN Cgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtp bnNva3Utb3ZlcmZsb3c6MTt9DQouSEIzDQoJe2ZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRp LWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1jaGFyLXdyYXA6MTsNCgltc28ta2luc29rdS1vdmVy ZmxvdzoxO30NCi5IQjQNCgl7Zm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1p bHk6QXJpYWw7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0K LlFCDQoJe2ZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0K CW1zby1jaGFyLXdyYXA6MTsNCgltc28ta2luc29rdS1vdmVyZmxvdzoxO30NCi5RQjENCgl7Zm9u dC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWNoYXIt d3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93OjE7fQ0KLlFCMg0KCXtmb250LWZhbWlseTpB cmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJ bXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouUUIzDQoJe2ZvbnQtZmFtaWx5OkFyaWFsOw0KCW1z by1iaWRpLWZvbnQtZmFtaWx5OkFyaWFsOw0KCW1zby1jaGFyLXdyYXA6MTsNCgltc28ta2luc29r dS1vdmVyZmxvdzoxO30NCi5RQjQNCgl7Zm9udC1mYW1pbHk6QXJpYWw7DQoJbXNvLWJpZGktZm9u dC1mYW1pbHk6QXJpYWw7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1raW5zb2t1LW92ZXJmbG93 OjE7fQ0KLlRibA0KCXtmb250LWZhbWlseTpBcmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpB cmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouVGJs MQ0KCXtmb250LWZhbWlseTpBcmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCglt c28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouVGJsMg0KCXtmb250 LWZhbWlseTpBcmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13 cmFwOjE7DQoJbXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouVGJsMw0KCXtmb250LWZhbWlseTpB cmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJ bXNvLWtpbnNva3Utb3ZlcmZsb3c6MTt9DQouVGJsNA0KCXtmb250LWZhbWlseTpBcmlhbDsNCglt c28tYmlkaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tY2hhci13cmFwOjE7DQoJbXNvLWtpbnNv a3Utb3ZlcmZsb3c6MTt9DQouZGVmYXVsdEINCgl7bXNvLXNwZWNpYWwtZm9ybWF0Om5vYnVsbGV0 XDIwMjI7fQ0KLmRlZmF1bHQNCgl7dGV4dC1hbGlnbjpsZWZ0Ow0KCWZvbnQtZmFtaWx5OkFyaWFs Ow0KCW1zby1hc2NpaS1mb250LWZhbWlseTpBcmlhbDsNCgltc28tYmlkaS1mb250LWZhbWlseTpB cmlhbDsNCglmb250LXdlaWdodDpub3JtYWw7DQoJZm9udC1zdHlsZTpub3JtYWw7DQoJdGV4dC1k ZWNvcmF0aW9uOm5vbmU7DQoJdGV4dC1zaGFkb3c6bm9uZTsNCgl0ZXh0LWVmZmVjdDpub25lOw0K CW1zby1mYXJlYXN0LWhpbnQ6bm87DQoJbGF5b3V0LWZsb3c6aG9yaXpvbnRhbDsNCgljb2xvcjpi bGFjazsNCgltc28tY29sb3ItaW5kZXg6MTsNCglmb250LXNpemU6ODUlOw0KCW1zby10ZXh0LXJh aXNlOjAlOw0KCW1zby1saW5lLXNwYWNpbmc6IjEwMCAwIDAiOw0KCW1zby1tYXJnaW4tbGVmdC1h bHQ6MDsNCgltc28tdGV4dC1pbmRlbnQtYWx0OjA7DQoJbXNvLWNoYXItd3JhcDoxOw0KCW1zby1r aW5zb2t1LW92ZXJmbG93OjE7DQoJZGlyZWN0aW9uOmx0cjsNCgltc28td29yZC13cmFwOjE7DQoJ bXNvLXZlcnRpY2FsLWFsaWduLXNwZWNpYWw6YmFzZWxpbmU7DQoJbXNvLWFuc2ktbGFuZ3VhZ2U6 RU4tVVM7fQ0KYTpsaW5rDQoJe2NvbG9yOiMwMDk5OTkgIWltcG9ydGFudDt9DQphOmFjdGl2ZQ0K CXtjb2xvcjojMzMzMzk5ICFpbXBvcnRhbnQ7fQ0KYTp2aXNpdGVkDQoJe2NvbG9yOiM5OUNDMDAg IWltcG9ydGFudDt9DQp= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/script.js Content-Transfer-Encoding: quoted-printable Content-Type: application/javascript; charset="us-ascii" function LoadSld() { var sld=3DGetObj("SlideObj") if( !g_supportsPPTHTML ) { sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis() { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans ) { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply() } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis() { if( !IsNts() ) return false SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) { nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.getAttribute("filter")!=3D""= } function GetSldId() { return sId=3Dlocation.href.substring(location.href.la= stIndexOf('/')+1) } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D32, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var gMainDoc=3Dnew Array(new hrefList("slide0002.htm",1,-1,1),new hrefList(= "slide0022.htm",1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("= slide0001.htm",1,-1,1),new hrefList("slide0035.htm",1,-1,1),new hrefList("s= lide0003.htm",1,-1,1),new hrefList("slide0006.htm",1,-1,1),new hrefList("sl= ide0014.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("sli= de0004.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("slid= e0024.htm",1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide= 0026.htm",1,-1,1),new hrefList("slide0008.htm",1,-1,1),new hrefList("slide0= 011.htm",1,-1,1),new hrefList("slide0027.htm",1,-1,1),new hrefList("slide00= 12.htm",1,-1,1),new hrefList("slide0028.htm",1,-1,1),new hrefList("slide002= 9.htm",1,-1,1),new hrefList("slide0030.htm",1,-1,1),new hrefList("slide0018= .htm",1,-1,1),new hrefList("slide0031.htm",1,-1,1),new hrefList("slide0032.= htm",1,-1,1),new hrefList("slide0033.htm",1,-1,1),new hrefList("slide0034.h= tm",1,-1,1),new hrefList("slide0021.htm",1,-1,1),new hrefList("slide0020.ht= m",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("slide0036.htm= ",1,-1,1),new hrefList("slide0037.htm",1,-1,1),new hrefList("slide0038.htm"= ,1,-1,1)); function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) { var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix(); function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') { href=3Dnew String(document.location.href) Start=3Dhref.indexOf('!')+1 End=3Dhref.lastIndexOf('/')+1 if (End < Start) return href.substring(0, Start) else return href.substring(0, End) } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ToggleOtlPane() { frmset=3Ddocument.all("PPTHorizAdjust") frm=3Ddocument.all("PPTOtl") if( gOtlOpen ) frmset.cols=3D"*,100%" else frmset.cols=3D"25%,*" gOtlOpen=3D!gOtlOpen frm.noResize=3D!frm.noResize UpdOtNavPane() } function ToggleNtsPane() { frmset=3Ddocument.all("PPTVertAdjust") frm=3Ddocument.all("PPTNts") if( gNtsOpen ) frmset.rows=3D"100%,*" else frmset.rows=3D"*,20%" gNtsOpen=3D!gNtsOpen UpdNtsPane() } function ClearMedia() { if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() { if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else return gCurSld } function GetNumSlds() { if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document doc.open() doc.writeln('

' + ENDSHOW_MESG + '
') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); function ImgBtn( oId,bId,w,action ) { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } function TxtBtn( oId,oeId,action,chkState ) { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new TxtBtn( "nb_nts","nb_ntsElem",parent.ToggleNtsPan= e,GetNtsState ) gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","nb_prevBorder",30,parent.GoToP= revSld ) gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","nb_nextBorder",30,parent.GoToN= extSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D new ImgBtn( "nb_voice","nb_voiceBorder",18,parent.= ToggleVNarration ) gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlTxt","nb_otlTxtBorder",23,parent= .ToggleOtlText ) gBtnArr["nb_nts"].m_flagId=3D "notes_flag" gBtnArr["nb_nts"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { history.back(); PPTSld.event.ca= ncelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; s.fontFamily=3DsFont s.fontSize=3D"9pt" s.paddingLeft=3D2 } function CreateSeparator( node ) { var sObj=3DCreateItem( node ) SetCMBorder(sObj,"menu","menu") var s=3DsObj.style s.borderTopColor=3D"threedshadow" s.borderBottomColor=3D"threedhighlight" s.height=3D1 s.fontSize=3D"0px" } function CreateItem( node ) { var elem=3DPPTSld.document.createElement("DIV") node.insertBefore( elem ) return elem } function SetCMBorder( o,ltClr,rbClr ) { var s=3Do.style s.backgroundColor=3D"menu" s.borderStyle=3D"solid" s.borderWidth=3D1 s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr } ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/fullscreen.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/buttons.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhWAESAPf4AAAAAIAAAACAAICAAAAAgIAAgACAgICAgAQEBISEBASEBISEhAQEhMTExAQE /KTM9Pz8/ERERPz8BAT8/KSkpGRkhMTcxCRkxAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAMDAwP8AAAD/AP//AAAA//8A/wD//////yH5BAEAAPgALAAAAABYARIA QAj/APEJHEiwoMGDCBMqXMiwocOHECNKnEixosWLGCEiQKCRo8YDIEHig2DxAD4LKD1avDDhgUuV GUOGbHBR5QGYFBG4fHAB58EKECJEwCfUYAWPFGAygLCRKQIIUKM6WAohKUGgCikcFWh1INWoYKVS 7SrQ41GbIhGYLAuVQVOoC+IyXUuUAkG1HE3KFDhAwkgJc5/qDZmxsOHDiBMrXsy4sePDGyP7lChT 5MULmDPnlDw5YmW6FTNrfgi0aNGEZPEtbfo2bNTUpYeeRph69dPWrqvCNFuBIGG1A59CYPAVQtwF cw0OxWdTIOiBCQAjaAB17fOFII8voGmRc+eOkilm/z9OvTtnjN4hYk1YoT3H2rnBOphPAB9skgq3 2lcaX/5YnJVt9BloAar12UEIRGCZdQghMABI1Tn32IQUVthYexhmqGGGMBHAgIfEhSiiiATAtOGJ GnYI4ogsEldicAYOGNJGZaml3Y0L3NTZUBz1xlB0PUoUI0jlVWRSVN89xBKSGB1YU1TMoRfVBEle hR9HQs1GEHxQ3RZZbveZthxt/LEmXHyp5XWABSCpaRJwbM13gAACPHVccgJFgF+NEhqUAEkQSCfc ddhVhh5dVTaEAEsTUNlkZUWKN9BNGDE6QU8OrSdbllzpxyVTTrU21Uj3scfhp7nNpyoDaTIEJ3P9 If8J2kbLNYegg9JRBwGhFvbq66+ZUiDssMQWK2yHxiZLrInKNotss8l+B5yBrr5p2UIJvortANoC 6+234IbLla/elRtZjeamh5CC3Sb0YLvixivvYkDFGlZqBNh7r4n6goVvv6/ZlCicN+kL71ALTnpQ dCIZp7CihkLA3UQmoWRBogyxtBPGCTnZncVR1rSTo5nuydC/Eo8kUH+lOoTyyvjoCuZu+PjYIKLD rZybtrM1d10C0QXKEVz48GrQkEeWdFJKlbb0UmEeV0SzyC6RvNB646LWIVjUNeC1zAFb+RDKXksM 9r531bwmpQW9+hQDDsx5pqwDRWBXcFES2hc+gEn/wJGdEEWdE6LoWcoxQweaTNmkhydkKaYMYY2Q p1unbLl/pPKbn3v7EZRvrKvqlja2ONvrtoIw9tn2g32/tQBlhtYkU+MNikZ7QYlPDPuMldpOmuJX nVo5VF3HjI+q89mteX5IDd/fVFClma5kiE4f2XUJhlz09gj2NbTDRifkmu7zXjR++RVJ/lPznuvr QH2iD6S+UewP9Dnon6d2NLwN8n90BB6hC68cFMCHoe+ACASP9c4DowUyEF0OPFcDI0ij/VXPaAKC UfhS95AKGoQ7IBRICI1HwhGaUIQoLGEKT6jCFrLwhSuMoQtlCMMZ2rCGOKShDm+4wxzy8Ic+DGIP B4cIRCKGMCAAOy== ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/frame.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Network Formation Game ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"

Notes

Slide Show

Outline

1

A Contract-Based= Model for Directed Network Formation

Shie Mannor

Joint work with Ramesh Johari and John N. Tsitsiklis

2

The Context<= /font>

Nodes/sensors configure themselves

To establish connectivity

To be able to deliver traffic (after possibly multiple hops)

Prefer fewer links

Dislike too much traffic through a node

Centralized management versus       = ;            selfish/strategic behavior

3

The 3 Pillars

Traffic:

Prescribed traffic from i to j is B_ij

Traffic must satisfy flow constraints

Shortest path routing

Bargaining:

Connectivity cannot be forced

Links are formed by contracts

Directed links

4

The Basic Model<= /a>

Graph G of n nodes

Nodes wish to communicate between themselves

Communication is expensive (power)

Cost increases with amount of data (but not with distance )

Connectivity is imperative

Number of hops is not important(?)

Establishing a link may be costly

5

Relevance

Applications:

Storage Area Networks (SANs) and SSPs

Internet/Peering for non-QoS traffic

Privatized Mail (!)

Part of the network formation sub-field includes: trade networks, knowledge sharing networks, buyer-seller networks.

This work focuses on traffic and connectivity.

6

The Node’s= Dilemma

7

Cost Structure

Every node suffers a cost:

Terminating traffic is counted, but not originating traffic

For simplicity all links cost the same (0)

It is good to be a leaf

Routing is part of the topology, we assume shortest path routing

8

Example

Flow through 1:

9

Centralized Solu= tion

One can try to solve the optimization problem for the whole network = and look for the “best” topology in terms of aggregate cost.=

Best solution is a perfect graph

10

Social Approach

Every node is altruistic, allowing each node to connect to it

Impossible to guarantee minimality of network – will end up wi= th the perfect graph and many redundancies

Specific nodes may suffer a lot of traffic without being compensated=

11

Negotiation Pro= cess

Two nodes form a contract:

Node i pays node j

Node j receives traffic from node i and guarantees it reaches its destination if possible

i compensates j for the excessive traffic sent through j

j can decline to the contract, but for a high enough payment j should accept

12

Negotiation Pro= cess

i offers $p_{ijto j, to form link ij}

j demands $q_{ijfrom i, to allow the link}

A link is formed if p_ij ≥ q_ij₌and p_ij > 0;=

payment is p_ij

A strategy s is a vector of offers & demands

Given s, a graph G=3DG(s) is defined.

13

Payoff

Given that graph G was generated by s

The (static) game is now fully specified

Note: it is not clear now if it is good to be a leaf

14

Routing Assumpt= ion

Monotonicity:

Satisfied by:

Shortest path with equal splits

Shortest path with pre-defined splits

15

Equilibrium=

A set of bids and resulting graph is an equilibrium if:

No node wishes to break an established link

Offer:

Demand:

No pair of nodes w/o a link can reduce their total cost by forming a link

16

Questions:<= /font>

Is there an equilibrium?

Can a given graph be an equilibrium?

What is the shape of the network at equilibrium for specific traffic structures?

How good are they (w.r.t. social cost)?

17

Stabilizable Gr= aphs

G is stabilizable if there exists s such that G(s)=3DG.

Not all graphs are stabilizable

18

Connected graph= s

Restrict attention to connected graphs:

Esthetics

Modeling

B-connected graphs:

Minimally B-connected: Every link is needed for G to be B-connected<= /li>

Prop: G B-connected and stabilizable è= G Minimally B-connected

19

The Box Theorem=

Given a graph, define:

And

When positive?

20

The Box Theorem=

Let:

Thm: G B-connected. s is link stable and G(s)=3DG iff

21

"The follo= wing are equivalent:"

The following are equivalent:

G is stabilizable

G is minimally B-conne= cted and

G is minimally B-conne= cted and

22

All to all traf= fic – many shapes
of equilibria

23

Uniform All-to-= All Traffic

24

Concentrated Tr= affic

Node 3 takes preference in
routing

Disconnecting 13:

25

MSDs=

THM: If G is MSD then

Lower bound is achieved only for a directed cycle

Upper bound is achieved only for a bidirectional tree

26

"THM:"= ;

THM: A stabilizable MSD exists iff

       = ;   Furthermore, only the directed cycle

       = ;   satisfies

Step1: Ear decomposition

Step2: Focus on A i₁

Step3: Do algebra

27

Uniform All-to-= All Traffic: Summary

a: cost for each unreachable destination

c: cost per unit flow

a/c < n-1: no stabilizable MSD

a/c =3D n-1: directed cycle is only stablizable MSD

a/c ≥ 2n-3: all bi-directional trees are stabilizable

a/c ≥ 2n²-2n: All MSDs are stabilizable; no other stabilizable graphs

28

Social Welfare properties

Complete graph: n(n-1)c

Best connected graph

Bidirectional Star: 2(n-1)²c

Best connected equilibrium

Cycle: n² (n-1)c/2

Worst connected equilibrium

Conclusion: Ratio Between worst and best is linear in n

29

Robustness<= /font>

A notion of robustness - how sensitive results are to parameters.

Measure as largest spread of accept/reject bids:

For hierarchical graphs – most robust is a layered connection.=

30

Ongoing work

Undirected links

Not clear who’s paying who anymore

Only trees can be stable

Convergent dynamics via a potential function

Bargaining games and sub-game perfect equilibria

Massive simulations

Efficiency loss

Modeling flaw: the hub problem

31

Potentially Int= eresting

User response

Fixed link cost – cost sharing

Routing as part of the strategy

Delay for QoS traffic

More complicated contracts

Realistic applications

And did we say dynamics?

32

A Contract-Base= d Model for Directed Network Formation

Shie Mannor

Joint work with Ramesh Johari and John N. Tsitsiklis

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/oledata.mso Content-Transfer-Encoding: base64 Content-Type: application/x-mso 0M8R4KGxGuEAAAAAAAAAAAAAAAAAAAAAPgADAP7/CQAGAAAAAAAAAAAAAAABAAAAAQAAAAAAAAAA EAAAAgAAAAUAAAD+////AAAAAAAAAAD///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////9 ////CgAAABIAAAAEAAAABQAAAAYAAAAHAAAACAAAAAkAAAALAAAAFgAAAAwAAAANAAAADgAAAA8A AAAQAAAAEQAAABMAAAAmAAAAFAAAABUAAAAXAAAAIgAAABgAAAAZAAAAGgAAABsAAAAcAAAAHQAA AB4AAAAfAAAAIAAAACEAAAAjAAAALQAAACQAAAAlAAAAJwAAADoAAAAoAAAAKQAAACoAAAArAAAA LAAAAC4AAAA1AAAALwAAADAAAAAxAAAAMgAAADMAAAA0AAAANgAAAEMAAAA3AAAAOAAAADkAAAA7 AAAASgAAADwAAAA9AAAAPgAAAD8AAABAAAAAQQAAAEIAAABEAAAA/v///0UAAABGAAAARwAAAEgA AABJAAAASwAAAP7///9MAAAATQAAAP7///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////1IA bwBvAHQAIABFAG4AdAByAHkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAWAAUA//////////8IAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMCL7uJqksUB AwAAAMCAAAAAAAAANQAyAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAYAAgH///////////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAOAQAAAAAAAA2ADYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABgACAQEAAAADAAAA/////wAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABEAAAB8BAAAAAAAADYAOQAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGAAIB//////// ////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIwAAAPIDAAAAAAAAAQAA AAIAAAADAAAABAAAAAUAAAAGAAAABwAAAAgAAAAJAAAACgAAAAsAAAAMAAAADQAAAA4AAAAPAAAA EAAAAP7///8SAAAAEwAAABQAAAAVAAAAFgAAABcAAAAYAAAAGQAAABoAAAAbAAAAHAAAAB0AAAAe AAAAHwAAACAAAAAhAAAAIgAAAP7///8kAAAAJQAAACYAAAAnAAAAKAAAACkAAAAqAAAAKwAAACwA AAAtAAAALgAAAC8AAAAwAAAAMQAAADIAAAD+////NAAAADUAAAA2AAAANwAAADgAAAA5AAAAOgAA ADsAAAA8AAAAPQAAAD4AAAA/AAAAQAAAAEEAAABCAAAAQwAAAEQAAAD+////RgAAAEcAAABIAAAA SQAAAEoAAABLAAAATAAAAE0AAABOAAAATwAAAFAAAABRAAAAUgAAAP7///9UAAAAVQAAAFYAAABX AAAAWAAAAFkAAABaAAAAWwAAAFwAAABdAAAAXgAAAF8AAABgAAAAYQAAAGIAAABjAAAAZAAAAGUA AABmAAAAZwAAAGgAAABpAAAAagAAAGsAAAD+////bQAAAG4AAABvAAAAcAAAAHEAAAByAAAAcwAA AHQAAAB1AAAAdgAAAHcAAAB4AAAAeQAAAHoAAAB7AAAAfAAAAH0AAAB+AAAAfwAAAIAAAAAAIgAA eJztWU1oE0EUfjObpun2Lw01/sMapFjRUtSLoqKYKiKNPxW8WjWhCUljTWrpQVooVPHkSQQvevEi CCoIgoggQvGgBQ8iilRQBA8i6E1MfG92Jt2sTd3URVu7Lww7783PezP7vTdvNpPPW6au317xDmy0 EzQoFOvAb5ExLFwxQYCAlBWKxSKJNCxFjxYUHYEs/vJgQBf04/MMDNuhMCuFoab0zn2Ej2cmQh6Z zXutfQ9tOPfw6tknrAHru/wKUwchDfGqdFpJB85IN5fYczJmGZZWUPr34PozcBrtOAGpqvWH0COs ++l0XEI+uVz/Idz5OOSgU/ycE66FVauf/HWDZtZrsPywjC9YykzUhP3p1TWC5+v/A7np/+SDs/n/ ZOzYC/L/OnDf/xU5GeOy/zM6A9XZ52QM+Y7y/y4YgEHoxZ1Poh39+B5ikjvraFcM1O+DaV90or8Z y1dZV+NqoTwOEKk4oGNbvRxnb/doYZPK3wi/YXAvpi+V83oYmd/kRvxhVcYfbok/bpB1PS5Ouyj0 47vjAZtsNLrWJcs8mu/05/ePud1/1P3DDVrI/vev9atvOvQ6KI+k+yCl5pQPUlygXF3lf3Rvp/O8 ST6D+GwByoFNfibyzv/5T+rdq3NcfeO7sxIgiiD4xKkNkaAN0nEBq0QrIaWOq5qZBVCNcZxC1DrY MimrL/Vr4KO1xnJCTJu/GVbIOxMh6RHWbmCZwkFttSbiqE8DdPfm+44On8Z05BIj3d/56A/TwktC q49D8GgyE88ZsfiQcSSb6e2HtZyNbMRiTGojgBGN1reRmXjepIf9F5bQqtfta48ryeEg9Umks0NK sqOe+iRT7UMBKflQw8Uo1eMWlI+J8iutct6S5FWzvc8TvXzeKM+UzRvl0/Oa64XC3NbLxPMLM315 k37P/7mVZkilFX+gxsq/537Rnizxr30mb993ETbQjp7hzIlsGkZ2oeBWUL9Wad9NOxiUdrKRprib VnwxQPxEurQjZe1Rfl626xIVukAOE9aYtgVFzAJ4ILDGOI/0DOfy8QyICLYGLjIV7/reh6CtACP2 Pap0JMV2x/ZDhfUzjHyaLv3G9u2D7kDdyZNnsrlsIm90DQz25pPZfmNzR6cIpdGekkyAXTEdm+Hb 1jsDVgsqr3+VMKTp8UvZ88tEGLafWirqGmOarvsYY6GxBITG0liyWIZAa2ZQj9IkBXA9NLYOpfuA j6+PkCw0lsLSjnw84mwk9YaKWlJz1pL6VQtKaCee5UxkvPXdD5j8nyJD7N5HKzKmUfs7ZMyd/sH+ ldHfwS+ay8cDETICWhr5eEsEdD4eimir7fjtfBqGhuN/D7+L/fyrJv7NFtEv8y3CLz/kFN8TMHn7 CQYznByPm/Rtzk6wt76E5/8u+r+X/7iX/7wx9JsLIf+xopxZ/tJX5H3/WTz0E18jAint68RRuqXP 6gAgAAB4nO1ZT2wUVRj/3hu2pdO/DFjKusJAsX8MNISeaKyp0dWgaYFujQcIpsA27sJ2u8xCs9G4 2k0wGg8eDPFYQuLBC6IHY8KB0MAROHDDw+oFD5hw8Abs+n3vz3R2uy1ToQh0vsnbmd/73vveN+/7 96a9eWNd8dzF8B9QRW+AAaVyA9R5+ph3QBsIHvWVyuWy5pcDeq5oFNJ4ZcGGKEzi/STkql1hSWqH kGvzNYj5dS76L0v2OxWDw+m7P5y+ypqIX699ah+cgPiy1vSSCZzR2lz5np85Hdg2gF7/LXz/FEyh Hkcguez1LeAVPu9nzkZsE+o5Chk4BeO48wnUYxLtMKLQaV+7Yv+H9cPYtqpgXovtYQ2/KHnuJsgY J2oBuc8NEMT6i0BPM/6LB4bvUPw3QxD/z0r863khkHmgVK6MfS/Vq/Gt6t4IQQ543oncgGLHwEbx S35A5zqyNdUGyvOU/8nWVLcpdqkGkA/gERDWAcUAwHqQMfUSUE6Q9WKTulN7GZ8j2F7Bthnm60lA /y9xlX/3Y+aPgwO7xOWfOjD/MuU/JM/vvNnQMhZ5BHnf58lJXR3rB/G/uolJ81fQ2mKnb/85NZ5N pCeFe0QzEvT1wz97fs54Rx1Kku3v888fSvytOH2s4dAWEf7XMhdS55G/5trh9WMbxbPBmGGazCo4 wGe6wWhl0IgoAVYhSZ5n8jODOAid2CpM1WLjJD6zA3FmIRfZZ3uAn+3F9WcGgH9h12xWYdQzl6Ra hR5YQiWxXszlRHHcIfCOsAq9wM8c27ZQsnoVBzXSqq04Bfl/da9POX63OcSnyflgUMUplCR3Pk7H Eqm4Y4/Ep+3RdGp8ErZzlt+Jzb5p5AE9hmrHTvQEut9jWm6Rd0ZIxOLx708uKLnM1fdgB4nYkdT4 3XbC3UlT4XMtVMVsQXpMfwuNGXDx+QYhw8WtAne7eB+TmGR21bViHVQZE2Qtu8/bQH7GXhI5lHG+ LZZzsvEUIRO2wtdiMP3cu2NBVwny1ftkLGKXkTdH9tL90fmjVDZM6QPV396URYcTR0+mnfRE1tbp 2e7v2yVK+dsx7HvW8v/314L8/zTzfxD/qzv+aZ4+++v/3+iEcPs1xMg8HCIefgkYFzhFa0RwqYA3 cP0kTwEhsQtUhuipj3WovkZ3XBOfNYpdltrRsDoz0JfEZXz6EdtsF8B7hvzioDFNMDye/XgsNxUH +EntOzz4lLl+xPFqi+VSR9InID+EHde3mGOL+ZG07SA/KhJOT86PvG9s864/fx/k7zeTiF4l988H nyyt5wf+/H2Alzu9+i4tF/X925++A/xFtP9XzeZnT9L+053mlZWwP+qZXwn7o75zvu3/qlff+fxM vY+Tn3/fThKcnMa/ij84j7o4vVmuq/HeTYRjLp7YQC7T42h83BLzXfylSTjj4o/qCE+5eEh4s+NU 17PlvdfCemYLOyQcjecipGciqfEvYeJHXXyxvZJ/az2rwJcaK/nf1Vfi35jENepnrXzyoV/7XNhC Is4n/wUBfZa5wQt/NwAWAAB4nO1YT0iUQRR/M59a+/ln101UROJLIpVULKFIMowyKMjC9SiV6Uq7 uK7rrspCsOqCRaeIEI+FhyA6WJcIPBjVtb/noG5dgg7dyt3em5lv+/x2tW8rKmPfMn7z5s9782be 770ZX76ofHf7ft17sNER0CCVdkGJpY1h4SbjAShWbal0Ok1NGpZ0gbYU9UEYfzEwoAfG8DsBcbsr bErV6AWmLDp//lx6yKrsPmEde2Fv0b47U89YGfVvM33qDIyCPy+dVtKBM9LNle85mbMTSxWY+o+h /SEYx3VchGDe+r2ICOt+Op03or5c2X8Wd94PUWgXP+dUi/YTBovAuf2E2+ViWdexrDnwk5QqFSDx 7sZvORTwvtXpT+Lfc+7hAcI/5ZQC/iX9Lfw/1WTdXDfNpzhg4pyOZzsWF0i8F+j/pB6IwCQMIvID iIMxjAO9iptyhErjJ/yfsHrDyUCHlK/+301bWb95f6dwUKTqFJ+t+Kc7QikWurdRzqc7AOV/fAJA JVAMBNgBMqY6jRWFmPJvEMMT03TpQ/bcXYN/TgeGJsLR8EjM6IlMDsYC4TGjo61duMJxX6ZNuIfJ tHXA50MPIlYvi4DmZlDKvMkAeJNB4TY6X2gCXg8UDyqeTKmRi6+r4fBwjahrjGm6jpOiwOcas0Xo fL4LB6ETe5PjubpxEp9rQT6HftELYg0LzViZ6wQ+a4CIaLPrizfZZ5lPc73JJpDLon0zscMUFs03 8hJaSZ1zGvUhkrTHjKytF72UhV3crMksLl7UHEWIWhurVW2lmXFl/JYGHkLcnhI31KmcT0hcxdpd LKsIzVOaRCyNKYPTg7FL/fFxDOfLQvcXDl8vkzq4Lp/0HDy+eOhieBQS3djwtkH/uJuzRCsW46WW ALyRkH2tTMaE/XoXHyqmqU1xJ/IGqvRXueUx8f1kkbtcTiKaldyZNbmTQi4Uodz+QMgfNXr900Zf ODQ4BhutU8plSm43L3GTCCNu8osVxHdm+INCb2OGX3IR35Lh3a71/WeY5JX9KXOdLK912u1/x1fE UQeCJn9z23r+EZO8fX/y05u9P1d0khAJmvz5EuLHM3y38O5olt4NzvuNM3u7+TThF7qCuvJWHWRU IpK6PCCfCisCA4zzBl88GvOHiNNhF1xjCm7Q/8ELe1KQsNuoQW7qPdp7kr7mupMN+ozT/aoySO1S 0G6H3R/y89tsf7haTyIGcu37L533aq3w78z671ULfxbnIPFCtwBDkA0zhg0zhg0zhg0zhg0zxq+e Ncs66+/79qOztlPOtCJyhi/T04NxfgCsI7zJZuDzww3ZmUGlo6gltWxKzPIv1b9B3wAE8wLOE0ji /DQNpGwITRxwLEQAFgAAeJztWE1sE0cUfjPrhGQTSOL8NA2kbAhNHHAsRE6FCgUVo5Yqpopz4BAp TYojvIqzJOuArBxSiNRDD1WEKi69tFRqJdQDFKEe4ICEUHsqucCxBC5cEMoBqYcSu+/N7GzWxoE1 4UdBftbzzjdv5s3Pvu/N2Iu3G5Z+utx2HwrkAGiQzVVDpaeOoXIF6gEqnLpsLpejKg01V5YNJYNg 4ScNBkRhEp/TkCkMhedKC0aB8kXvn/8tI+SGNB/2tl3+6/LIr6dusVqyb1IxdRQmIFHSmF7RgTMa mzux56fPB6hNoMb/BNefgpM4jzEwSx4/iIzw7qfffuPOkzvr/wJ3PgE27BEf/9KK6ycOBsD/+om3 4YAs66grPuIk6+hmbL8FtQ4k78uyseVN8v/SvU8t4r84U6pkXZn/b4f/jytkWTcANwAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAGAAIB AgAAAAYAAAD/////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMwAAAEQEAAAA AAAAOQA0AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAYAAgH///////////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAABFAAAAWAMAAAAAAAA5ADkAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABgACAQUAAAAHAAAA/////wAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAFMAAAAuBgAAAAAAADEAMAA3AAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIB////////////////AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAbAAAACIGAAAAAAAAzZv6Ux5QPKfXU41K abrM83dXojAFMzCKzE8iDyYxD8QcdMoXK42XiH/i6n7mp6U/KXX8Vy0beXx1f6fcTTmgBZXyM/Fe 5QC6I9Sg0r3Ne/7jTwBoAMqBAI0gc2ozUE4CeM/x+z4+21C3om5DbUfd7tjKeeXtC8M3oekyhgrP bnqHA8mvpi3bGk8b0amZ0XTSmjT6IntEKByKu3UiPBSI9MGTj36f8kbZFGh1DGpYcD4JwXmTwkbn Z7sxFVBMcNhyc7uTD/rvtMCjgRZR1hjTdB07DXq6U9fgfAjd2EAuijkOYznuWqLYbhi8LYLzPcC/ Ob7jWc8aToORa+DnQ6g9WDhjOGqhTrtYdqZ9U9xhDhfVb2SjDzEaf6sgGzJJu8tptduElQ7gaq5K 8hQXv6g5uhClCGt16mrcdrX8R+3LCDGuq7IOmUXjSSbewNJFVCMCcESTjKU2tTAwmj4xlDmJ6fyS GPs//uDprNjvBUYc36v38/N1VDFoKxyrJdzj4tAmwnEXRzlNKeTiIyD7S/+QlTuwIO8mHOqHkqmE bcQSp41BKzU6CTs5m+tFNRa1OcAbD+1fL7am5zKTuWevvsS/30UeTFvhPztp3KSp8B8dZI+6+Gp7 vn2xTfR3ca6e5dkv6Pntz1Xl+1sI5NuvMNlfrvPrFbVOEca4zngmNWZNwFw/VvzSph8ovk5w1slA Bp/52sLaXCushYTNNea9f615y33Yx/9poCWHMoXxVMzfuaCe8Pe+0W+jiDtffnGeH79of5Xf2d0l zXfc73xne73zXY2H0uK+cL79/FiYPNgZha+FBL9cbH8ox1V4wBD8dLG5NZ+f/7bm8/taUPh38ZUu wj+bCn+3WeJCPsM6+dzdSS6GXT5xXeIifFrX/o2IAyXsrufzdsLdZrWDf2imHta0YagWVhPt2Cre Vyk8uLgrIDwYdBuivKqDPD9J5OzrQf6pdV1ka8b5jnjGTidShHTogG9FY/pafhiErizMBQi5f6m+ nHh3WVujTexg7LPilv8Ba+D3NADKgQCNIHNqM1BOAnjP8fs+PttQt6JuQ21H3e7Yynnl7QvDN6Hp MoYKz256hwPJr6Yt2xpPG9GpmdF00gAUAAB4nO0YS0wTUXDe21LtUi1tBAnh8NDEi5E0cvJgIyAQ D1SkJF5ZTCtLaBfaxaYXpcEQ4sm7iZ+LRxI9e2g0XtWDBxMvEGO4mqgnpXXm7b61acRsCZHUdDbT vpn35s2befPZ9t3b6NaTZ33b0AAJ0KBaC0GwjscQuSK6ADpcXrVWqxFLQ6y1oaVgF7F62Idow6HB NFj42CBgDHL4nYdSYyn4K/RgFajfz49M1ec6v9Cs/oOGVtZ/kPdPvYG/cTpExZker197qRSojBZf M+oplYDDY3AVFiHd7LE90IGzZu2PIZ4ApX8U7c/CEp5jDhaa1h9D/dQDVe/zI4OtEzLumLv2T6Hn 01CAuHz8Q69rf6AJ/XTWhOaMld9IXvUCwiNIHwUnV9vw/8IYLMMKGJj5JuZBDutA0qVu+cpKgRFc v5/fuH3gd6EP2I/+g4RW1q/e6SnPqQbQOz3VZ5X/IaAaC9CJGEY8hngcMeLKRN3vdp1oTeiX9//p 5R03HsRuD8ykeuRYY0zTdRZbGwEtwqATRybE1rBJRkHn6wngG3Hg6+8HeHkKeNlAtBHnEbEslDOI eUQLMSt5JO/M2S5fyP0cHs3lXN5EM7FPrSzgxjLR6jfqBjb5h0j85DSHkazdZmRtv5ylSA9xNXK6 uPxFy3ELORpkvS6v01sX5rP8cYzeIM4EI9Dn9lzq6BUcPUWcxckgdzKG1oRh0rDnZ0pLWE6XpO4f fLXqnPC+1Brg0DVjZtMFkUwXxbSVNXLw4dHX4jaiEN+Lw92ZTbLvHHNy8ry+yi5GSXKipOhQhOgF jy6HiTY9elx6Z6Tk6Be1/eln0s9fvHNssdOMXGMuNNoFTdrl7CtvSZ73VYRu1cyJtLJgRVoocoq+ edyhlcROmCSEbXkSQ9IHwlYrrodISyZvZXXFCdKdTuH9CM+z1zSSiht/sIiTRalSds5aRN936x3z n2M+PbXK0gHa4qOh6LOc6IShu3Giy1iSjnOjpEtWYYAXMvoY56dSpYKdzsIm6aG6PAD3mMqEuzsx aPSmtkfWJIeTV5wRw+qt6W7eNLy7n8SPSfNG3ipYGVuMLa8YtmnlxNBgXLaCyymPJ4NdEYND8O3C 8+V6fXvnE6v7S+k3tPPpX+XTL9D1LHuo38+PTNXnOr/QrP6DhlbWf5D3T72Bv3E6RMWZHq9fe6kU qIwWXzPqACYAAHic7VldTBxVFD737rDAQIHdstDWilOwtT+UNFYfGlPbRoEYU6qliQ82ylbZdFlg +VlKNtEUWkTjU33Q+CIuiqtPmhqNtqWKJk18MNUmJhp9KE0l6ptJ64tV8Jy5M8vMwM7eASK04WwO M3fm3nvOveec75w7fP9dYHL07IZr4KCHwQfTM4XgtzxjyNxslAHkGc+mZ2Zm6JEPeWaVbis6DHH8 JUCDeujEaw8kna7gShXoBeZcZH9+WXjIhHjdYO175tkHwpdPXGJFeD+Qb/rUIWiHVk8yraQCZySb G74nMyaIXA6m/Edw/R3QhXocgzbP8oMYEdb9lB0XMa7cWP8TuPOt0Au79J88rcP1UwwqIL9+slMq T9wXIv+bw0emDS7BvmtAxHsxrMb6nUD/Z/xPXLpwkuKfcsr+IvFsNf6XJ/4/KRD3pt40nnDAjPUA 6CkeSiF7nBOEU98Clz6rtLKpHrqhD8IY+VGMg07EgSajdUIqKrUF+D/F6ktMpqcceZW/1HQ7yzfr d4p1wgAqCwifKbYprqk+UJEJrinnU/6nOoBwgTCUcGKtMUcVXkNAOQGgEgibANYjb0C+C3kj8t3I m5DvAfIdMa4arzXI9yJvRt6CfB/yVuRtyNuRdyDXGv1XaemI4Y76VOFDztxNNjwYfa4n3huPJLT6 7r5wIhrv1HbX7dJd4dHmzDPdPcxG3W64uefjbquXDXYAH9QgeDqqX/lgAjlO9+QTHK5/HTXw4JWr FfDDU5X6vY8xn6oqjLHg6QbwlXIoYjQFMD4cRKdRfUzX22f4LjNiwTyjlqPz/YyO3FNA79CTfXsU krZRf0ueXsjNO5FF9RMtxyn0uzq2znhWlOlXzLX8iQqqILb4S9GzSZ7IlBN4dxZ5AN3/il9EDPUp hoPhxPEjyS6E0wFGsm/xvOnrug5n9CO1wqGsOdlxLN4OMFShjr75axB+evtG/zVkTfurP1QZqaH1 7WQiJu9Xx1iA09CtyVzzjYXU89nnY+ahvuxItKO1V2tq7dcOxzvCnbb+B0KRD83+dP0zo8ck3kXa 4/2ilWaNRTRdY3uh0Z7Kp/7WHn0KbWVbzGy/qK+jMdNu0BVqiIl1aQaenRE1Tg49reuy6zmgVJbT DNGY2Y6r9naAWdt+fqvM3o6p9rbZX+g5MG3qOY89Pzg+ld2eQk9m6KkpD+pyd8bM9vvF1P4m0+7z U3tvZr/Wr7H2T7Nu471z/+bxi69IL8CIagR+qhaDsw05hv3e2IqMwMuH9+KTCHI7chy5H6OQmVEY 0ANQTGAdFKyWHMRPHSVrZz4pzZIZT2nkFlTSz+ePp655tIZ50IKyh1Xu7Grd/aZKuZhHW7ctZ5yh nd/rcolbu52rlKuqdPx+kX3eufq+Xiqtb5rmXa7674pMR0nyKn+p6XaWv5T1H7FM/bdaw60cWin1 36dGz/2+SnjhkLX+cyn+EM5J72z13/PogCPYeCbPrP8+4ouv/1q4lrX++wx5EkOgMku+aoFcuLw9 oCr/OPB+XygSttd/I9L139Mh9fPs8zFY1uSPUheb/53JnyhXnThbz87Wqqk5tWrKUaumHLVqalG1 qtUG9hwOjtoTHLUnuNWeHuQ6a5IU27eWpjiaWd9bZCyozVnjoo+NfzuV3cfs60s5ataUdM2KsVGY XY5zPTchyoQc1fAcFQTiEQlZZSD+DTWu+yDjvLo52Zto7YAwzUuZbxO8qg+gP7//FgTnmnxznVen pgNNj2V5taLIbpsRdk6y3kVb5LnhlN0WI+wXyXoXfemcG1459U0WS+vr96JvLCCt73kv+p4MWfWd jSlvmDE3dh8qt2PVjwGBVSa69ZU40U2c1WXPKy+XS59XvvRyXtlcsfD9cDtH39D1bUwWGu3XAvb1 a8qTJdYd05THi6w7pil/5DtHJBX7iEFbPtAUMx+YZ3G7TdIOm6SFTRaScPnw9ur5MrZ08p0dJGen hE9g6Q5jLX9nsHUhOcjNbqNGzjH3zJ6T0pmctABMryG5TkwfugMx3QvZ7Twmjf9DFeo7bt8p7XYd k8Z/xI8Lbt8rnfrK4j/q+64XfWXxH/Ud96KvHf9d9R3z8j0pJP89+KJ13v8Ab80HJQAAAAAAACQC +AAuAC8HAQAAAAAmAAB4nO1YXWxURRQ+M/duu72ttL2l3YJQlsVi+SlpJEYh1ihKSaO02JKoUR8K 6Ybd7naBFtoNBqutVfFFVH6eUBIT8cVEow8kUIuIEh/Ax8qLYDXGRA0J/sQYu54zd2a5e7u3vdtW I7CnOd05986c+WbmnDnn3K8ull8+/sHCK+Cg+0GDiVQRFNieMWSuhDKAIvlsIpVK0SMNOZWnG4ra IIF/vRCEjdCNv7sh6TSFKakKfOkz18k+LlgWMmq9brL3vTr23OWLe8+xedh+oFjZVCvEoDOnOe1k AGc0N5e252XMauT5oOZ/CNcfh52IYxtEc57fRI+w76eXMcuQw7KBAAAAggAAAIMAAACEAAAA/v// /4YAAACHAAAAiAAAAIkAAACKAAAAiwAAAIwAAACNAAAAjgAAAI8AAACQAAAAkQAAAJIAAACTAAAA lAAAAJUAAACWAAAAlwAAAJgAAACZAAAAmgAAAJsAAACcAAAAnQAAAJ4AAACfAAAAoAAAAP7///+i AAAAowAAAKQAAAClAAAApgAAAKcAAACoAAAAqQAAAKoAAACrAAAArAAAAK0AAACuAAAArwAAALAA AACxAAAAsgAAALMAAAC0AAAAtQAAALYAAAC3AAAAuAAAALkAAAC6AAAAuwAAAP7///+9AAAAvgAA AL8AAADAAAAAwQAAAMIAAADDAAAAxAAAAMUAAADGAAAAxwAAAMgAAADJAAAAygAAAMsAAAD+//// zQAAAM4AAADPAAAA0AAAANEAAADSAAAA0wAAANQAAADVAAAA1gAAANcAAADYAAAA2QAAANoAAADb AAAA3AAAAN0AAAD+////3wAAAOAAAADhAAAA4gAAAOMAAADkAAAA5QAAAOYAAADnAAAA6AAAAOkA AADqAAAA6wAAAOwAAADtAAAA7gAAAO8AAADwAAAA/v////IAAADzAAAA9AAAAPUAAAD2AAAA9wAA APgAAAD5AAAA+gAAAPsAAAD8AAAA/QAAAP4AAAD/AAAAAAEAAL0RdsEe6MCdjyCObjyHFint9bQr wRnMX4t8SbYN5L+nsZEJyUS3geXvpSCuAChHLoG839+o9F/6/5b9I9/m/f//5f9qnLoHJlKTye7/ uhyT9/+bg8zBCJiDUeDDRSFzcBOZBD+8TxqHoWF6x+gxf2G16GYOdlGHOuQV2BhuxCdh5BhyArkP tFIGxYzUom3YFAyvDGVTYIY8Krg+SOScSA+3Bzfu2tPRG0l0A90mSlizFn5d9+EuL54gdPHpe928 pHJ6yt3Jt33IlPMXIvvByvHpbqANJj+n+E/3t93/TeQKsO7USqCYABBArkZegLwQ+XbkRciLkWuQ lwDdXQBLkUNg5RR3yN/l+Hsnch0ynfdK+Zwo2/2Up9mROnuyBZKVQ8zHw7uEhrDBT+/QErSlOlnL IvGWLKWIqxZnTLYYRxWitYZVy2fF6X4lPFg4WkUWs7ygFC2D5rMsaRRb7yMPoPlcKLAsjvqUwOaO 3h1bkzsxHA4wmvsv7psYFxheE+arcyhrT8a3JWIATwaMg0e/M2HsrWt9V5CDwd/6xivDp2h99cyy 6buMvexPgbcuOZ2+WMA4666PiX27atN7hC4sWDGtXsT5+lQ4Lb0srfek3zPez3LB+7jhGe8bueBt LvWM91wueJ+p8Iz3zZ2e8dboldwz3s/d9Trx1uinfZ7xHsoF7zeGZ7xfTIVXRlRzsAkDL1eBl/Hh VZCP/7cA/Rvxf6YxOlv8d+rKx/+5JS7r7y1Y+XdCDzSIP+9ULSO/+vbrddyjvhwmmYbs65k7rbfG /M54dajUc7w6nEu8emm+53h1Ppf4WltlxzswAVIvPSW9WyPxzp5gS2dfsC0R7+j2iDeoXxN4NyWL pHywnHqEY4k+1eOxeXRvRruU/EixGNGlRvxY6ByR1DNHPM+tEUpuErdxk5T72QLT3r+ffVxqn6Gf tZdkztDPaotEj5jqcdbn7NFpzRlT8uJykp+O0h1P2bYhrMmKsNaelolYAHBKxEnGeag92dPbGYdT tH8UHZbCATGA/g39YILzrDQX22t5sKUZHOfmtIehKuPEju8z7aEyEF6mzo1hhNAMWbc4vj1SDbo5 sn13oicR7k3nCsG1axpEKMshf5iM651K4wzhoj3iMP7piOx5oiAAQ60B0dYY0wwDs5e4LamhJMgl saF0SsPzYT7GcJ8daVlUpGVmaHJaJpWm9ZiD29MTisnAYNe/8/it7zyMv9wgtOS//3jreXMS+Y1b /f8RJnX3YZw2fKr+f5HPvv4f1S+Xu9X/J5HfRntN6tnrf5i2/vcHjFec9eTvVeFjmfX/CPda/5+p MO511+eMRyPca/2POA88Me6OMzMenWamx/of8a5z1+vEe5pVF2ePn1nwvuq8h93xPqXvE3XvL0lL 5pol/yzl95gl/yTllHaPiG0XpfwJs+QLUh7lrTrJjRJnMOWGE9e/3h2nc/0VLFpIKupnlD+4rz+l Jcqs/EHJy0S2EImq9cn3adn5/llxLtvTcsjIfL/fnzl+U4HIHaJqv2ScT8vrhXfHo879y22dzv1b wttKSEM0quQNhXY5qDUxC3cW+5rV/taITKchvf5jQl49kzzmGM0zF3nMjZj/SbuIzcQu3PPyAT0g 8udITMkJI1MuZ3Z5jH09L1Nu9mfKU9iRsy456vT/qfL8u4Uf1it71d8V9nw+Le8RftUYVfv1h2Hv 38/kvTTJr5y4sK750h2Xc/96tYjYn1Uz8pup1ntcs/xE4f8HMW7boQAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAkAAB4nO1Ye2wURRj/Znav7W17j16BvR61HNcXyCONhFQakPpoCSRt5REg +lfb9MJduB7QAl5QUy0SS7EVQ9A/CNXEKBjjK0hoAlhshb8ohL8a05CSakyMComPaIx3zszOLrtL 126vBa3pd5nb/XZmvsfMfN/8Zq5fyx1959PALTDRYyBAMuWEDN03pG/gBcjm35KpVEqtT83SjKJN ECe/NghCNbSQ5x5ImJfCP9I8cGhzLhAeD2H2vV+prtG3rTEAMQAwAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIBBAAAABAAAAD///// AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAhQAAANQGAAAAAAAAMQAxADMAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgA AgH///////////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAChAAAAiAYA AAAAAAAxADEAOAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAACAACAQkAAAALAAAA/////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAALwAAADcAwAAAAAAADEAMgAxAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIB////////////////AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAzAAAAHMEAAAAAAAAyjv/wvV9X6EcykjqmqqHndA8KZ16kgAj qhvztWenTwEpc0DV/yTxPwa7iB2NEJ20fh9gw5q32y/Mn5j7/zQZ+WZohXL2s09+4j+NOxHs+0/b fpipvNNp+MvGOkny4iHt3aDEPEkB4ILZmJ/J9CDj/85LK92z8a/QfyX+VbsnygOz8f//pGrYDXuh gUR+hMRBC8kDdZzbZysqg2mu/6/tNrRB6eifTprJ+mnuoLmT5m4a0w7ypJifpocsUpygpGqK9Wne pvFO45/mARr/uUBzIEAeKDl1LtA9AUAGmpsA8rnc+fyZvE/reJbSowI2/2NfXuTr4VSGDAfrZfYu ICRIEvJ1xEDwIMgmbxHwdUTprEsCWTnkwzrS/fgiUhaTl0NrQMAIkAMhhDGrryFdMetKuiF8yBcC XV/88lLQhGpyfB1NmkKmDCRNNT6UFWJaEX61nElRvzuV71TOgcnFDl37Itw9v2Jed4Ys6tUkICQH rSORILyC6WgVsFoaKU6svim7MH1DmIhgb8uRn3/L1trl4H5xNJdGTGmGBwJ8z6aR1E/e+kh5m/ib EJWIo21yoLahbceWxC6ajhHV/Sd2JMeYDa+z8BUxeDcnYo3xnSRmZanzrW98MNz78/5bpASDv+7/ bV74JPVvGVJi+hHpIv6D2bsoMZG8S3nSo9byEBu3Ozq5b9K5hcUTyiV2Ht4+Zm2nIhdxuReQL8u2 vaus5ZrtvYD82Xp725NgbW/Xjm/t2vuseMBBRfyUUHgsKPyPnD+NFP4HzqeECg/lr3H+C6TwQ5zv x/Ui5ddwO4MpKzuJ/5XWdpr9z0PRTCpi2T3+M0xJ5G6JxJpbg3XN+4Ob4rGGFpv+p4S4l0pYp/lX 5KYhEImq/vF6jTfXP8/mpUnjQ5Kx/sUsY/91GZSviarj1Yz19f24kkV3LGoev8n5aR6/BXhTDpUQ jar8E5l6PijUIMXucdbXlMa30ElFlGv+n2T80qjEs4bEMotyY6fo9oIC+c+zXETyc2hzorWtOQYn qR66yy+Ew6wD/Tv4nQ/MPgswPtU9XreePkdGRmBsbAxu3LgB586dg76+Prhy5QoMDg7C2bNnoaen BzZu3AilpaXgdrtB0ZVMCRLPu6azI92FaiNNe+Kt8XBbsHr33oa2SLwluGJ5OYMiT23WvrFkqTLL V8Avqz7brbfwAxgeHoarV69Cd3c3bN26FYLBINcPGExEdi9wOp3g9XrvKXqqqKiA1tZW6Orqgt7e Xjh27Bi0t7dDZ2cnnDhxgj0bGxshEonA0aNHmf/hcBjWrl0LsixbjCbBXxkZUFZWxtoVFhZatnO5 XFBQUAChUIi1LykpYX6pPH36/X4IBAJQXFwMRUVFkJ+fDx6PBxwOB5Pxb+B/OuDb0YTNbNNk9U83 zWT96v09je0AKBhluvH/AlIo/n+I6yrkzyB5LiSFQEIoIqWYlBJSSkkp421m6f7Sg8m/1vhfPX+s 5vnglFOGOXWm80dt+uePbdr5IzKufuq3Ff5fTxZtBwmIaKaK/z8Xpo7/wdHvt8L/Z0hpJ53OWOB/ 74T43y1LfjNeD8jhI0b8fxM/gxU8rfCC2CTr8ZogynP1eEsQF3n0eEwQh1zG+odz9HhLEG879Xhs AHH5Gq/KH+/8R2dJf3Icf+YmOjlGLE+OetlT3f+VVb0EpnqqNZ9e7e7/6ni+69PPzwDakKufnwH0 nsc4/nGXcX76JGP7uU5j++cYvt7G+VF82YCvR3EVi57atPD13fVpxtdNYtKjx9NN4veSni/CG/KQ zu4iXOk28qcz9XyV8P4U8Lg+jox4XBA3uBT8rY7XZa+RXymljc+PUL3Tgc/Ho4nyiUzOvdb5xDxf N/HvNs//JE/lm8/p1uN7CZ22ef4n9h6xlmu29xL6ONu2vYHJ2FvpsW3va5Oxt8pn29759u1F4sVs 2/Z227cXiYNue/crxN4C872Ftb2l4gi7P7nN96vjnNfuW7CxPiSMGO5fPkIjhvsXQVwyT3//MoAU fkjj63OUexI1331i8z6GjFePtV/m8dom+Ng8LOF6ZPSGW69XRigr/fua8cbzb6UUtp8BAAAAKJDW AhAD2AJmaIVy9rNPfuI/jTsR7PtP236YqbzTafjLxjpJ8uIh7QAmAAB4nO1Zb2wURRR/M3t37W1L ez2gV0rBo9UK8idV4h8INRilDYQWQ0kg+oVSr6GXXq+lBbyQ1MOaxigqGgN8MwZFMUbFoInGmCLK x8IXEz4YU1KNif8wUROM8c73Zmb3dpfbdu8oIKbTPG5+OzNv3r6Z92Z+y4XzVROvn6q9BI7yIGiQ yQYhYHnGULgBQgDl6lkmm83SIw0lO1tuqbIVkvg3BFHYAH34uwdSzq0wZakGv7nmtDf4uNwhY7K5 xdr3wjvDT13Y9xUTe0o39tQW6IVYQXNaiw6cWd/Hy5g7UeaBMf/D+P4J6Ec7dkG84PnDOD/FgLH3 vYy5A6Vb1bl6/0fR8zEYhCbx573UqPf3FTA/+f/dElmncf9Y/JdRQs2lKEGQS5W57jtxttyMMpPx TzEwVfyPHX/gJ4r/OQAzHv80K/16GTPD8W8787yOm8n4p/xTaPx/7Jd1w+4ysOeBfMXIDZUg8wFe AaAKpQJmz/1btWyAAdgLnRj5PRgHfZgH2hXa5ykqo0Xu/x3Ma8/pSzHzz2S5lec37vSUuymHUFrI d/5TfqD7PuVuinfKAUb8h1Hmgsyp84HOBIAIUG4CWIBSi7IQpQ5lEcpilNuA9g7AEpR6lAaU29Xc jep39s5x/UudWP/JL9apeHw7GIF57RFR1xjTdJ2FR9pAq2RQhrUeCI/EadV1DQfgg1YcfmQpyjKs jDaDxhkwP2OMc9G+HYdyNRQYHw3jYufG8qdXgKnUoidcHx5pKWJkeKTLYiptTt00mo+W1gt7mVV3 XOheDoXpjl+lOyh1U/8DhcQfrYERe0xhg2NvxKAZwYCMl1AbRqL2kUarVSdaKVKD3KjJWwDVGEcV oraK1ahnZWa/cg7+sRqK2MZAJUYmzScjeQxrp1HSOOi0T0Y89SmHts6h3dtS/XgchBjN/Tf3ZyaF DYdF+vBxCHWkEruSvZgbInrNse/CcPG13/dfQolG/9xfG+k+RO+3ksmcco/+LX+M09Clqen0RSL6 8+76mPDbbxa9V2gVYdm0etHOBTsm3e2UepnSe4adLPVs7yF3vU57z7D3yzzbW1uIvWsrPdv7QiH2 rg97tnehd3uZ7/Myz/a+6N1e5vuywmpvOgPu9tbt/t6rvY2+b/yk4nJK4iMK/6ow5/b2ek3iXxR+ j0n8s8Kab3k14fMKn2USj5t4SznhlQpP8A98hJvVe0Wzbu+F/nrJ/b2c/tquhcU6LFfzRNgrFdZ5 I4yVSuz0p+AgOO+2nkRsMNoe2x/dmkx09nn0p+bripCGVtMfkfmUsnriBl4q9nOXicfn2NvvEv5p NfHlIOGWuOE/pd/Edv1n2Rthq/6zbFOVvf1EpX18co5d/ye6vf/8oL3/kwHC2+PG+p3j1vYJvl5k /7a4cz0L86tzPbt8GWF3PG7gH3UrbuCb5jKL3Q18bYUdnyyx4vXaW0y+Z554uqb13yT8ucL017mQ Hd+rS0x3UTqVdHFyyUuLtCUE8pPWZ+Ksw/tHfUdqcCiWgEM0L91il8BzYgD988wPYXD6TIP8pf2h 9o0uTagrk9V0dW47vn3QLaqtp2tPcjDZPRTdMLC3c6gn2RddvapJXKUf6TCficPWAKtWwx9rPhxw m9E5f+6TfDHlZvA/MnjrLP/7T8xv/P+Nlf/R9+nrxf+8cLpZ/nfjyo3JX+4szuCf96l8cLE8Ats6 qkVd8U9ik5pkkwmvRPQJpGP9eTrLFo98Fu092An8YK+SaI4VMv5sE06zDtFA3mmaIa8BV/FR8rsb /3sZg+pVDMQhv8H/PuXXzv8mAmNVOf43e/5f2/nfau4F9y3nskvyfz+AG3v+kxdz/P8EShotGw3k 5/+Hp+X/x5D3XXHws+Nzuzfb+f8w+4t543tfV+sD7vqc991hdtQj/0c766ay074/h9kp3bO9ewqx V/K6q/mpl3u/u70QeDxk5VMQqKyw8hMIxASPGzBxSvDRfoXHNDXexPbxY9ruUnv/Fr9VX5rdHbL2 T7NFZVZ9aXa0VPIdA79pmz/NYtzef62I2kRR/Mjd/zsDDUGrnTsD9wesOOprDNqxz9Y+wTJBO+5y tLe450vnflzs5OlTrW+D4HXnzfVbI/L0OhMvEt8HjpvrI/uPm7hc9G82ca3POh79X2Idn2Yblb5i 8r67/3Ffinhtytllw2k2KeyOxoMKH6igLN3Z2xsr4iTYTJZYTwIquZMg5+XpToL/D///F8At0cUA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAW AAB4nO1XTUwTQRR+M1sKXX4KRYEQjCsmBA4SIgeDURN/gJAAKpB40INF29CmZYEWSENiiogHvWiI PyeJIdGznj00Jl5BEw96MAHxJ95M1IMxtr6Z2Vm2lZ8FDYr2Na87b+bNmzfz3vd25+lcyfzdB5UL kEGHQIFkygVOSx+xKhQD5Bh9yVQqJcdTWdpS1AU6/qKgQTP043MIYpmpsCqVYRZIWwrKdJby/oQY brHqJl41XXw28oTwnMqTOXUcQuBb15pWUoEStjY1cs/OnJ3I20CufxT3H4YB9KMXgute3wM0Left zvMbT2rs/wSevA8i0MB/9qkC989w5wD7+2fn3+cQbfb4bvE/aXAuiBC5QOA7S/8mbSr+901GsvgX 9LfgX/ot60AW//8XNcMgDIMXkR9AHPRjHeg0pBFbqNQ2kP8Mq/ftKNqk9a7/u2krry+/31ntdhjt Mnxa8a8i5yMXIBciFyG7gV8BoARYDQQoBVFTt4O4F9ipGdm68ueJYKQUVeRQ5ru7HP86AueG9Iju j2rNg8PeaEDv1xrrG3gqHOs2+3h6SKG+ET43PRxMSzPPRJDlikovn6/2THSA4iaQTzwTgSpg9WDx 8VWp+a4Mnp8q502FEEVVUSu8pG9aUjBzsaMVp9+sRa7DRqbxVZXHsXSN+5F15CFD9iKHDNbANAET gz9bBeYa8/8bLeZ4AXjED5BQWt0di0R9YZi6Xu6fYgjaBVfM6/Ol9x6OtT1EnLvEnrw/U0PvCALs Dgo1DjaGSFRKKTutKj7KUOaisiW+AviNnKIJ3qonFUZfvqlXQM/SRBFDbI3TDZXGNwNDcgJb95Dj CG8nFYhnOgXQ4Y329cQG8HUwAGK/OclF7sM1tih1UCjujoV79RDWBrd6+vYbD7yY/jS6gKxpX0bZ Gcj9spqyV71AvnJ/a2Nr2assV1Mr2yP83D5a7N5ioYa6Ne2in2dW81PYJabdG7m2/YX1+Nvosvob T4Jhl3/Tod2eQNgX0Tp9o1qXHvb22/Q3TqYLWcgDQSmTPGax1ZTHcpjcYco+mj6+n2djOCj80lIb 8ytzv/PktdPq1zxpIULO3D/84v5PFjITWtBlyB/yGcq8oZBP9rx0sTl+fUiTcyZ5LDR9GV8yY0z7 3tqNcZy0OZiJGV01EKWCqLwAS34rsDx1Hu5ss+oJm+Dc7Wbz54JSbuL5ecCUd4g1DTmhCP1ZUy7g +gdNudJhnY/5kGudb+5hQ3GaKfW3L3824HRzvDYs+ZUmx8miOz2OY0Uyjsud5hrVuJ15slo1thuN Jdqk9+eKRMTn9IbpB8oqU8UAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAA eJztWE1oFEkUflU9GTOdn0kmmgnBQxtB9GBQc1oPS3RNxEPiTwQPenDUGZxhJp2f0TCsLNGoLO7F Jey6sKCIoEdRb7KHsMuCB38iKOze4s/+iJeAehB1xveqq3vb1u7pmWRjEuYNRddfv/dq6n2vvurJ e41TF6+1PgKHfAkK5AshCNr6mH1CA4Aq+/KFQsEcL1RkQcku0PGXBQ26oB+fQ5BzhoKnNEOVtecK tvldLvonjOFu+9zJO+cu3j/6O6vBemfQjKntkIZ4STbtogJnZJvL2PPzThTLUjDtf4Xrz8AA+nEA UiXbjwD/IOb9vpeQTy7XvwP/+TgMwzrx8y8tuH7CXQD8r5/26duAUQ9heVckRvKy1OPcOjDwXgsV rC8GmUv8dwZvnq3g35D5gn/Tb688UMH/4pUuGIQjEEPkJxEH/ZgHemXrqC9UamXG/xW/E31IOfZn UxayfcodlDsJ05QSqrBQal6CpRoMfkA8n3I2YZ7wT3kgDOIKAI1AORCgCYycSnqa5TP/P8VsRWZP lov9f/Lrd2ZA/N0MD/ZERVVhTFFVFhnLgBJmUIO1JETGUrTrqoKRgx1b8fUfV2NZg5XTh9oiYz0+ Jx/H1HE8gUXHMiTbMSxpWTSwVHjHPp1nAfjv/snl2GYM0PPYWBWgMYxkpYnTapeLUYr0EDdrxilK NcZRhai1sxbZV2PNq+X7+UQ9RfyqYBha5ZlLSJjA2mUsowiPIDcQQ3NqoSeWPbw7N4DpdEDYfsOr 8k+ED2cF/AIcGvpymQN6GrEVVvf+9DQCf1x4MfIIi6a9Gvk+mhin9a1lBiY3qN+w18Lf1bli+lqj asFdHxP/27RN7znaKlhTVC/6uc/LT0Mvs/T+sMS3v1CKvx0hu7+jeZB6BSdCvbuTmfiw1hsf0Xbp mVi/T39H2YU62vJkymyzatK41Wp/XUXtHqsd5x+ObxTRmEkZfmmF8vxyrneKPQ7a/Zpi3cxoO9cP M1z/zjpSoaVCsv2shlAWS6fjZs+fIXonoQ9p5junxF5o+id8ce4xP/yX3z0eZdsCpOKSrkpEqQJ1 xtcow1aDOK8AfhE4ZZy39eWGs/EMjJNeOsFWwBnr89XJfyLgXLcCn5beTb3bXIaEMDzpFFXmHcfd h7JoT/LgkD6sJ7Ja1+CRWDap92sd7evEUbqlz+oTycJstHfAyy+uD3pZtdsHXnyWu3wO/kcOX52J 0w4p1f5sy0K2b36/XQYGFmbK/+jEtPO/Cgec3zI3+cud/5n8c1zO3BGKwrHt/vkn+e3G/wJNBv/r tvjfylnhf52NXvyPIFE+/9sbVaNvHfxnJJqYduF/RfX9tkzV3PUxVztOPnCjnlTfTTnO5LJ4h92+ 86x35R1QnHeUwQ+myRcnP/i3BH4wJ/cffrq6Tbz9scz0/Df5zc9wQny+bXnYodx6td5tuRVZZOJy //OTp1q88pTL/c9Pvlrhla9c7n9Qzv3PK989D4v73Ly4D7qvv6T7oHP/Wm/jHew91HcD/QAAAAAA AAAAAAAAAAAAGAAAeJztV91vG0UQn91L4vicxPY1rZ3065IWSJQ2JC1CqoSQEI0rHppCU6mvcYOt Guxck7gJFq3UYlS+EX1BSIjWEfwBlBf60IeqohJPpRJCglAEVah4BInygBA2M7d7x+1Rl3MCRUEe a3T7u92dnZ2d3+z5+mfx7xYv9N4EnzEAMwA1AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIBCgAAAA4AAAD/////AAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA3gAAAIIEAAAAAAAAMQAzADgAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgAAgH///////////// //8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADxAAAAeQQAAAAAAAAxADQANAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA CAACAQ0AAAAPAAAA/////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAMBAAD0 AwAAAAAAADEANAA1AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAIAAIB////////////////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAEwEAALkDAAAAAAAAPAoaVGthaPO8Y6jcATGAVvmuWqvV6JWGWmvKmpKDYOGvCCaM wTQ+Z6HkT4W7ygbMAscWnT+/JjLksuhOecdWPpw///n8VdaJ7VNhJ6cOQB4yDa3pFR04o7W5zL0g c/pRu8FZ/3HcfwGOoR9H4JmG1zeQEd54Bp2XlU8u9/8kRj4DczBi/4JLEvdPHGyB4Psn3j4XEu0I 6u8Bc6UqNQqC81gCII7aBU3er1W5l/y//tTAB8R/ulOa/BfyX/Pf8ZvmUx1wON4OguN0TDpqCJoc /z/KGMzAcUgj83PIg2msA+MSzQdipbmC/CeuDrEgI4NJo+v/07KW13e+36l2Uw0wUak+E9+pBjj8 p++EDlT6dqP7nr4BnPvfQF0HoqauB7oTABJAtQmgB7UXdSPqJtTNqFtQt6JuQ+2T65Nux/Z9Ejfl 3gjDaGu6yCH/3U1nuD83NWvNWdmiOTZzPF3MWdPm7uEROxX2Trjv7PRwwPBuuL3noxk1z+Kg8zND YJRToEU5RJhRxsuWccoJDstXorIejIQScOJAwm5rjGm6zrxzcjTnjIE3uK7hDHyzD/gLO4B6+GlT PHEd/vIo2n17AHUQE7Q8Bf7VPeNWbPHpfoPi5nCHSS46/5G/QaPnEDwcoj5kkvauRrvdZPfSLRzm Tkvc4vY/ao4m7NYwS8p3EXdcB5/kla3EuPvbosgsWk8w8TK2PkadRGoluGAsjemA/eni0UOlY1jO J+21f+Ot1WXbh7dY+fAqY0s9/HQW1UKdlTiNmpcqZtavP7xeXxDZpd+Gq90Uu51Wu8Sf6F4M/JKN h9z+HBP9uoyQDoIJJCI+MRCfR5ds3xjn/ROluWKmAEupnuwSVcQ+eNW9wV78wbDPfycTefAT2tfq +Dv+2PgTq9nvvyC8hUNsolQ4YuUBzib1pXe+N+DL8z8v3EQ1zV8WaM/O/kQMz7E4p+0PlPz55Lf3 bI/+en17TMbrT7sPhMjE4N/aRT+/vpufzjk4di9GAvv7RiP+XosF9vdGI/4W1gf2981G/C33ev09 VQVp1/4PgXYP5QqZOXM8s2AetArp6YD+VtiPW8hCruTg0aSKTyZU/JW9v30ufmQd4cMu3hUnPOXi E13q/E87Vby9Q7W3GCaccvFrIdXeFy3q/D4fPslVeykQ9kTczNrK4uY/D+CFbu+6wPO6iuNMYP95 wSrPa9E+L7MUlnjPZqpY6Xw+47wZ3Ehzstas6cbMzh3TcnEP4VEXLyfU/l83EN7hYjOmjh/uUsfv 7VTHl9rU8S+1qOPf08R4/5k0Fpu/nsmDEbHuHWLu5/S3R28F5XSF3Up676EKe8gg/L6LR6Jq//Pt Kn6lVeA77NdfE87W90vd7x/fpWTMAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHgAAeJztWM1vE0cUfzObL28SkiwpWAikIYdKIGEC nIBSimgq9UD4CFKv3kRr1ZbtzYchMq3UQKSoqkSVv6BVL720l4J6qyBCAnqogAOVUE8JpS0SQkJq e2lVu+/Nzmx2jZOsXatg5GeNd97sm33zZt/vzc++d3dg+Ytvtq1AhbwJBpTKMegIjDFsXCv9AKYa K5XLZRoysJVb0lRyBlz8FEDACOTxOg3FylRYV7ZAu//OKTf4HS9Dlrzb7wRtxUdF58fzNxnl1Fy7 zqmTkAWnJp9BMYGzYDxR5ryGbRC0/+MYfw4mcR3jkKnZv4X+CQM696PM2YwtpfpcxX8Kd96BGRiW n+gSV/G31eCfbL82Vvv/BPavpFonjneBh+2WvLrSSPxTSq2H/8VlNkn474bG45+80jXKnAbjP3Tm RZ3XSPxT/akV/x+qg1yvOwbhOhAUXRN60KYXWjXhVZIRmIJzYCPy04iDPNaBUaWdj4RKUWf+345q GEHq8d9IaWb/mtNT7SZcU1kmfqbPf6oLxPOpZmv8b8LWB/InAAwA1UBv7qC6tupD88h2+f5/vvGV yodTD7fA/fe2yr7BmGGazJofAQEAAAIBAAD+////BAEAAAUBAAAGAQAABwEAAAgBAAAJAQAACgEA AAsBAAAMAQAADQEAAA4BAAAPAQAAEAEAABEBAAASAQAA/v///xQBAAAVAQAAFgEAABcBAAAYAQAA GQEAABoBAAAbAQAAHAEAAB0BAAAeAQAAHwEAACABAAAhAQAA/v///yMBAAAkAQAAJQEAACYBAAAn AQAAKAEAACkBAAAqAQAAKwEAACwBAAAtAQAALgEAAC8BAAAwAQAAMQEAADIBAAAzAQAANAEAADUB AAD+////NwEAADgBAAA5AQAAOgEAADsBAAA8AQAAPQEAAD4BAAA/AQAAQAEAAEEBAABCAQAA/v// /0QBAABFAQAARgEAAEcBAABIAQAASQEAAEoBAABLAQAATAEAAE0BAABOAQAA/v///1ABAABRAQAA UgEAAFMBAABUAQAAVQEAAFYBAABXAQAAWAEAAFkBAABaAQAAWwEAAFwBAABdAQAAXgEAAF8BAAD+ ////YQEAAGIBAABjAQAAZAEAAGUBAABmAQAAZwEAAGgBAABpAQAAagEAAGsBAABsAQAAbQEAAG4B AABvAQAAcAEAAHEBAAByAQAAcwEAAHQBAAB1AQAAdgEAAHcBAAB4AQAA/v///3oBAAB7AQAAfAEA AH0BAAB+AQAAfwEAAIABAAAHo49BN/bSYM1n6K2bfOEI8I/3Ab+IJeBiCpuLbVrpNrasagL0PH7p sLov1PhE4Mn6qTT6vKVd1RL9XErUmvNBoT2g3G9TWCBd/8Y9hgn9GSoZg+4hEoxvGe3WdnmXkBLj uuedwtRjHB8hewkWV2Pdvl0PT/KkRYh5vaMPtqkzm5C0hL0vsQm82cE9xJFND5ywC++fLU5iOZ6U vv/mcyVvhYvkFNo49J9N55wZMerMijNuzs7Dg89/n13BJsSfs9fjKZfi28M8TO8359ijAZqaKMaU bvfSLgghHG3R20sWh4W2WOqqtMh2eRZaf6uTSQs940E7zbCzWUePfG/QOlLutD+nYMg5rr8uTvo+ tzJOVlOcTL7PZ4F4d8t4bd/PB5vCutND+oSv34+F9U876RWmM1pPyGwZz3jrFOX61glqnUytc5kd 7GMBP8vsghnWfwJvHVXygJPfsWJu3M0CPImbKz/8YkXen5L0e8SP72h3WH/IPN1UWWnKzJXpp3Ky X54ZAN/JXGecD40VZwpODlzyS6fITviEadw9/s2Cyj0woLqMHht9l67V6hfDE8cwFW4rfntQFTuR nph2Z9xUQYxMnbMLaTcvDiSG5VH29pg/JsGmlcQB+OPglangCtaunyzwl9jG1i+fvAj+Rxs2EsUw otTqv9HSzP71/7e18L+N+F2L/zWP/D/1c23+p/nnLmW5+FcV/kksb6/HCxecIWs+j1drSLLP/8b+ 1ud/JQTBUxw8xDX/29EA/reEPGkt/neLNPS6wKrzv+G6+N/leOp0mP8l2bUOyf98vdQueZevvyHj 2VvNX4hnzG41j1fyjFV/lTwjyQalnz2+/qvke1ef8xOFRwXjCvOoJLPa6Al5X38knzjh64fk27ah Dj5zmvwG+Qx9rfKZ1Zg34jMt/tfify9a/gVkH3lmAAAAAAAAAAAcAAB4nO1Y20sUURj/zhmvs5Y6 iC5SMvkQhLjrJR+SCMM26EGzFKqnXGUtw931smpCQSTIEgT9B21/Qvbgi4gECUFUDxE9Fl1fgiB7 Kdrt+86cGWfH1mZ0IZT9lrNzvjPnnN+5fJff7ssX1W8fPKx/Bw45AQqkM+VQYmtjWLipVAGUy7Z0 JpOhJgVLpiC7Ss5DHD8J0CEEMXxOwpzTFLaUWii27pxsgz83LGTVeH3a3ndw+WLn65knjGxqVTFt 6iyMQcQTpl1U4My+Hzdj9mOpARO/G/cfhXFcxxBc84yvIT75gGn7bsZUYBmRdS7334cnH4EpaBEf 9+KX+y/ygE83dEM6Mo37bTu/tCylYPh1Qfa25NP/yQe28v++m/Uh8n8V611FRlu+/J9Q6elmTJ79 PyvnuR2XT/+n+OPV/9el/5vrLoPsOGCKGQ98YMStQkzYWxKCCZiGMHr+KPpBDONAr9RmXHmlvk37 D7nt6EK2g59P2c34Jn+n2E0xpBgL8TPK/xQTiONTvPbJfvvksxAH9oYcAMoH7x8fkfZw72ctvLpQ J+oKY4qqMm0+DPx2ELT5YeALkUZtPoZPrZEnW7E9gB2TSQgGg9u2XdP2mNTN35hpNMKv2NjJ6R1a onKQ0WoPiLdkqeXcrBlZkGqM4xSiFmB+2eaz+lXwVdZVqmHtcEkl1MuciT9mYRVra6Qh6gIzLJ76 VEBPOHF1YG4cw2GLwP7Fb6XlaREoFHGoGhiNRqb03sisfj4eDcfgzf3vs++w6PqP2bv+kXO0v2Zm +FSbOshWSmhowNLTxaS3WvpxsZ/g3/A44fXPRYfiYwCzdWr3s49aDjwmzvWbDbdG4DRb+idO+qNN OMzjvgwcZs2rFdEMMUv/IGYctvROcdthEVvolFVxE+I45VqqRAwCWBZ3xzhv7J+bSkSicI5wKSod gjtiAH19+ayBc89KDpvrPdl7xqwzjGaKKu3OwV3JC3pGhyfjU/GRhB6amA4nRuMxvT3QIqjQqX6r TRiLqQTaYf3Y4kQOcIcw218qdqFzojWlmo39MXfTeZb/kf/p8C7vbNlZ4hU/37Kb8b3k/0os9vxf BYXfA7td/nf8I9xc+f8KohxFZdHK/5fykP+Bd/ly5f8l0nAvS3nN/yf9Iw3Z+T/Froult7aY+prg Ax3W++z8r2e2h+fM/+vwWeTltn/yiqRfferkFfZ9ZOf7FEuW0RRNlr6SxTNSO+IZufeTYguldp6R cvCOlIN3pDbxDpP/dkubK6uog4H+WlHfgv8qGAt91Ywn27CfarDhDjCYcRMIZpx09TfOTvO/B97U QOdo500kG7xp407d8KaC7A35A/KuYnQAAAAAAAAAAAAAAAAAFAAAeJztWE1MU0EQnt3HXx/FQkUk pIenBw9GG5ATIYhEMXoACZCYeOJB2tCm5fFTINULP4kxHownjxovXvSiiTcTG43RAxEPxBBPgBpN vJCgJ7HPmX27tS1gXpGEYJjmy9vZnd2Z2Z2Zfa/v5quW7j+uW4Y8Og0apG0PlGT1MQRXTCVAsexL 27ZNXRrC3qc9Rb8Q6d02Yp92jbrBwl8CDGiHIXyOQjK/FPyVarAKZK/nZk7apZxbKlT/TtNe1r+T 5093A3/r3BApZ/h8tmz9ncDg+4lXjO6UqWKnj8EliEGoULMzpANnhfp/CFENSv9Z9D8Ow2hHP0QL 1u9H/XQHqrvPzZyDiLBsc+l/F+58CMagXvzcU630v6gA/ST7SHPaat+oT90FhFLky8DJ1X36f6kd RmAcTMz8CObBENaBTslNuMpKAyM4ez23cfvaraAL2o7+naS9rF+901M5oFynskz1WeW/B6jGApQj vIgKxAGED8QnAFQB1UBnbrV87teMvUMBcf4fXzyU8dC1UgMLlw+LtsaYpuvMP9sPmo9BObYi4J+N 0qnr/HoL8BsNwKexBEyHERZiVPImIiZhgJrHZ5rluCH7B7JWVqtS70ZJc1NJ1DMThH/87KTYL5K5 QLz6xm3DgL6LTFSjMcwE7Smj3QqIUcoUD1ct5y1AfBFzXEK0gqxW9pVn5Ly8j/f5KWOOlfigTt7Z lEkpbD1AGDhYwp2MIxkvdJiJwd7kMJbjYaH7J59KOxbeJqVQxKGyNxIPjRmdoUmj24qbQ7B4b21y GWEYPyaf14Yt8u8kc3L6lD7FPlXR1GDSI3mzgnbBMIyQkqioIIlmQ0mkyvIlYmWOhOLPlDIhoWYs FtMMMxYLqZ43GtkRtkYzcxKamGNl7OLEN1j5frKC/GTiPFez/D0u/DUzeq4dyOVDXuIHMvyCJ5e/ VUpHGIkqPiiipT/q2GnY27MTpJ1M2rnEmnwsS88Su6rn8h/AsWOTOOCktycZ77diAN9q9eW5z37X +5MWelsy/rWW5/IrzOF1GZW6iFwRfjImK8WdAfBMxDrj/GhPciwRioNFeukWOQI3mUwt+PrFD/l7 oMHm1NnWeXGLITyFtK3pMm/zvj2oinVEBkatMSucMNpHxs1ExBoyGoP14io715PpE8mmmGAjfG96 MpKt5QoEAoEt9P/5S8wN2fNoKEFzsA42EFahVSAF3hQBRV8SLjDHt74T9FzzrfvmWgmrEimt3s4B aBI+AVxTYJ10aRvfD34DvJthQQAAAAAAAAAAHgAAeJztWV9om1UUP/d+Sdt8adf2W9eWMcZnBLc5 1rXdBlNENmZFYcvGWhSfJK2Jxi1f2iZpjchoLZQgiHvywQedCL4MBs6HvWgpEwvD4vbmHjc2t8EY CFZftInn3O/er1+ypfuSxT+ZOeEk99w/59w/55z7u+2Vy53XPv9q83UooedBg3whAE2uOobMldAB oMu6fKFQoCoNudCguqLjkMRPGkwYAgt/JyFb6grrUjf4nTMn3+A/2h6yaDe/6O5rnvv93k9T3zPy qQM+5VNH4SREK7LpJh04c6/Hyxh0XegCZf8Qrj8B4ziPUXi7YvsG2qcYUL7vZcwG5Jgsc7n+Y7jz UUhBv/h4p165fl8F9umEVmQg07hV1/7lJTdjfQvYsd2gx5dqGf8UA+vF//jGO3AV4z9Igt+uq1X8 k1X69TKmxvFfdOd5HVfL+Kf8U2n8T2l2Wc07AMV5wE0qJ7RinzZo5ITHiYZgAjIQwciPYxxYmAfC UpryFJVmlf7/utcxADQAOAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAACAACAAwAAAAUAAAA/////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAACIBAADEBAAAAAAAADEANAA5AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIB////////////////AAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAANgEAADkDAAAAAAAAMQA1ADQAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgAAgERAAAAEwAA AP////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABDAQAA5QIAAAAAAAAxADgA MAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAACAACAf///////////////wAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAE8B AAA+BAAAAAAAAI4eqBr7taR6tq/wO6UDyiGUlgmfqfuf8gLhfMrZ7vhvl7+NXFDftAXoPrhx8ZD0 h5bWHhgZ7hZljTFN15kxFwH+/m4w5saAz0dDxpwFGp5/sJPx3CD5B583Qjy3D6iFz+8EnhtApmss v6D5898iL2gsv6gVVr/TVleXkC8hL6NMc1C+x6Qvqzfmm+hwe1E4z6kNPVF7jdFst4hW8tQAVyX7 FqQS46hClPpYr6wLOv1aOfADQQNLTzW1w2Z5ZxIiWMTSBZLQ1S8w2+OpTysciaTfGsmOYzrsF7b/ 4DN5e4anySj4OHSMxBPRlBmOTpvHk4mIBVc/+3X6OrJp/jZ9sDe2lda3i9kxNaifYe+IqQ/0K3mp iVTtc9qfE+vZLe2ZhersMbGvvzh2V+C2j1QMPmgdnPQOZxOjyZMAuV790vLPRtl12HqZM99cC6nY 6cgLfpJ3OfItTvLX99llj7SeM2y+mTRYjmz4iuWbwsKYIz8rvCwichqdri48QGyrnFuHyH0A3wif YZyHhrOpdDQBW2kelA2fgA+Yyp93bhtQuicaPJjCB8MvAxTna4ZZVNOl35dg5x78OhIfm0ymkrG0 OTSRiaTjScvc09cvUvELw06dcFYl9O2BlWfOT7gtl49/5vqTjqL9T+7X/oZU06D/IP0b+I/+/nHa S0ePVKn9WlM9268G/9HtSfivE9Yw4EZovAvrkf6Z+6c6/He2C+BVFPZqCv99UgP8Z/JFoxz++xJ5 BhuXyuC/YxIj+PM3xBzux01t7fqnf94sxk1nN8XuFuO/U2xTOw3dnn2Yvotd+g/l9ZXioVNsm0Eq dmSrwanueRbjuxmW7SQVA1klv7JB4MisLuXxAO3u4bh1IuWM6Q5QHzOu5HPNdAzJWFDK73LKMuFM YjQ6aTqjugRSNDMPQ6i4M8ulCLX8zsywjzoEIs0o+ek2kr9w5DCz5WoQ6no796E4acuxYyNQK2Mj UPX+SkuffynQA+8d7RFl5/1Fr6o3QnwWL9vZMHIGOYE8ihxFngS7LYkck+XDyHFkHDt7Ajll68AH m4b2pVIj9Kj4j556wD/ejrwDoPL//1WEwO/SPrsROH2tIfC1M68Egf+/6S8pLB7JAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABIAAHic 7VjNaxNBFH8z2w+bRlOX0pZSYe1B8NA0tSeLWKVG8NBoP8CraUkxtknaJm0IeBALRQTBUw9exH+g oF5FgqKnYnPw0FNpiR+9CIUmIDXu+t7s7LpEKxsplJa88GPnzc6833y8eW82udWTG8+et29CmVwE BXSjAeocdQzBLaUJoFbW6YZhUJWCMKpyqOQnQj/oQVTlwGQYEvhLgQZBiONzFjLloeCf0oJRwGnP TR/dZTu3Uin/fsth5t/P/afcwD+YGSJrvr7qbLvxfevJ2vw7Rjklq5h1DK7DFEQqHbYtHuCs0vmf QDSDxT+A84/BNI5jDO5UzK8iP+VAK/e56eNFTMgyl/O/gSsfgSQExM+9tMn511TATzt0VyZya92o v5ULCPVgntOqHG0JwgzMQRhPfhTPQRzjQEhq865OpYbe5LTn1m+Dbhu6kP/h3085zPzW/Z3iF8UA utNTfKbzfwzRABRjARplu+PyWY0NR0M6gPJB/s1Z6Q+Pd1vg481WUVYYUzwepi6Egd/vBnVhHPhi pFNdiONT7eQPerDev7dvTU5Owvr6OhQKBSiVSpDL5WBpaQmWl5chn89DsVgUvmv5HpO+bH1j6uiE 37Cyj9M79ETlFKPRdoi35KkN3CqZWVh8kXI0IUp+1ibrGu12Xp5ll+pVLJ2p80G7zJn4MQtZLL0n DVkXmenx1MYLg+HU7dHMNIbDgOD+we/pcrWIFGo4NI1GY5GkFoqkteFELByHtac76U2EphXTj9om hmh+Xcw8U+c8t9jrOurqt3W9lvQeW78g5tP9Nz5OfCOZ2FhiCiDd6hlY+azuwcfEum47eJsFT5et f+Gkv/yDh1U4L5OH2XbVGrIQt/VPwuK4rfeJ3Q6L2EKr7BE7IZZTjqVJxCCAV2LvGOedI5lkKhKD IeKlqHQaHjIrhm19VaF8zsoefhm6HLomi28ZRjPFI/2u7O5Kp2AwOj6bSCYmUlpwZi6ciibiWq8/ IK5wV0bsOuEsluLvhcL5FzNOxpX+bZ+JrBIwnGCOv1Qs2YZ+o6QYAoax43OihDZKvt/2yvsaq9iF oJgogQEEtCmQBW+WQHMn/AJDxBGzAAAAAAAAAAASAAB4nO1YTWgTQRR+M5tGs40aF21D8LAW9CA0 Te3JYpWiETw0SlPQY5OQ2JT8NE3asOBBrBTx5MG7Pz0Kgp4Fi6BH9eCh4KVFxYtCQT2Jie/NzoQl mrIpYmnNC7Mzb/7evJnve7ObN6/3r95/HFqDJjkFGtTqPvA66hgmrpQAQJesq9XrdarSMNU7sq1k HIr4q4AJUShgPgtWMxQ2lB5EgZqLzp+/shGybDefc/adTF55uDL/gunUrilMXYAcpNuy6RQdOCPb XGLPzZi9mA6Asn8G/c/DDK4jCdNt2zeQEc79dDsuI3Mu/b+IO5+GMkTEz70E0X/ioAfc+097dVUS eTemnxvgoyZTN9g878jOkn/J//XTzx4R/+lO6fDflq3if07yX62bxlMcUHzfBR2+/w8ShRLMQQKZ n0UeFDAOxKQ274qV5ibw78c06qajS2nX/t+W7Wxfvb9TOKYYQO/0FJ+J//Ru4AOKsQDq/t8j805s 2BnC8DQ13cZQ893di4+xbGq2WC5mKma0NJeoZIsFcygcERQ+G2/UCXgoJTwE3048KbnHrsIek7r6 xryDIPyClcc4tSEStYOMbq9DopWQ6uOqZN+C4ouU4xSiFGZBWdfd6Ofny2zVa2DpqHcfhOSdGSCv sfQS0z2E/yKzEU99/DCWqExNWDMYDiPC9g9+rWav8DYZBQ+HwEQ2ny6bsXTVHC/mEwVYufu1uobJ NL9XH/gyS+RfP7M5dVyfZB4vDR20lH5SrH/A+sP8nOaPW/lkMQcwbejDUx+NFvMzsY/rDjuhLpqi v2HnMyd95Dc7rE0/bDusYSfooRkKDTsfxIyphj4sTjdh6XJXdbDRR2KvJSBiDsBTcVaM8764Va6k 87BEdikKHYZbYgA9bnwyoNlnrQXGYqOx8610ss3h/fMjUr/8rgfeXuoVZY0xTdeZsZAAfn0AjIUU 8MURzAuYG3385iCBjNzePP6Z4y+VrZBf+LC0OQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAW AAB4nO1YzWtUVxQ/9z4nMW9iPl7TaYxJfImaD5pEiasGIqk6gqVJJJNlqCY64gxOZsY3NgwtpM1A KF0FFMGCEBE3Lox2URCKBGp31fgHuLBdtZsSSnFhdMZz7sfLZJzIi7ZKZM5wuffcj3Pux+937n3z cKn28dXbDb9DgRwAA7K5CijLq2OYuFZqAHyqLpvL5ajKwJQryaaSEYjjLwU2BGES83OQLoTCKyWA KNC26Pz5A4mQRdl8JL/v8m9X7h2c+pVVUnu5xtQwnIXwhnzmiwmckW+usOdlTDOmOtD+D+H6Y5DA eUxAdMP+LWRE/n56HXda5Vyt/xjufBgc2Cd+3qUe108c3ALe10+8nffJsonpuQecZFWqAsn3asy3 QYnvm13eJv8TT7ruE//pTinxX8q75r+eN42nOKB5vhUkzyswL4cSz99XCUISzsM4Mj+CPJjEODCk tC89sdJ+DfwTV1uYl57eZKP+/2vZzP71+51iN8WARkwUn4nzFAOI//RG8GOidxvd+fQGoPsfPwGg FigGAnwAMqZ+CHQnAHwEFJsAtmNqwLRD+WlSefZ/wnNJNiYMT8MwJYYK7246w8HIyXNxJ346ZQeT 58dTkfikvb9nn4DC4ZBbJ+ChlZ798O8nPybzUZYEo5qBn1mZCFiZqICNyS91ACe8caj6xafiQeJu AB59HhBlgzHDNHGQA3ym/WUTJp/tx04IYiuTKNY804XlIr5NMgfC/6VOLMz0Af/WLpqszIg7Xo61 Mh2wOiXaN80dpriov5EXPkYdG7/wURsyyVjgtNpG0UoXcAXXJXmLiy9qjiZEqYfVqzq/26+Szxvz 7cS4trJqZBb5k0xcxNINTCdwaZ8ZkrHUpxIGx1NnRtMJDOe3hO8VDs++Fvs9x4jjveYAnw1QRXvU VPqZKooCthDd5+k26tPn6pcrxRhX91WQ3uXqw0y2m2omJkjEgYozK7wG5DPwZ7E+xnlrKO2kwjEQ UacFvmc6Ro3+aUFbFqZpn7vRLuXLTP7nUEyGPh06uk7TGimOmZB75kE85zHI72FlOoHPnmp9GRkK ik4etDz4X/1L5R0Jx19NKB2biJ+F6QGsONRqdu3mbLobk/3QmAZ8kcp9l3dCr9nPTwrCdqQL8VTM 3pxt3i9ub/UctV1LYKxT4eOPZ1+9wi7Os3u9eUq7TNnt4z/tFvP1ZBfn+8DbfNFuW/58v3kut3RO vsnR7mgkFnbsofCUPRKPjU+Ct/kO8At7yILj6k/Eg2nE1W82S79a/2476SFXv15HsOpwtN5rifGu /pfgatLVj5eRnnD1AcE6x1Hnm329dRXu12O+tIssRB2t8yaaZySq9X8aqD3o6suBte3+OjHe1Zv9 a9svlq/V7zCpF57POnja6/V8/t5JJq5FtT5F5If+aOF+wRvu10QjmRgrNv83wtcP9SJWR18AMU3k pwAAMQA4ADQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAgAAgESAAAAFgAAAP////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAABgAQAAAwYAAAAAAAAyADIAMAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAACAf///////////////wAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAHkBAABVBQAAAAAAADIAMgAyAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIBFQAAABgAAAD/////AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAjwEAANkFAAAAAAAAMgAyADgAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgAAgH/ //////////////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACnAQAAsAUAAAAA AAAAJgAAeJztWF1sFFUUPvfOdtudLd3ulu72h8K0RSgp5TfRGI3BQNtIQlFK0vjmgm3YtdvtHzYN MS02YAIvxER8Asf4YsKDoiY++BN+1MSEIEETSdTIj0beNLH6UGDXc+bObO/dduosqQhhT3M6c2bm 3Hvu3O+c881e+iZ89e3TddcgT54CDTLZAPilawyVO0YlQIl9LZPNZumShpotygMluyCNf6NgQDsM 4HEYxvOhsKBEEQXOWLT//KJAyBlxu0N+dvJIw+VtY1+ycrpf5mBqJ/RDb0FzyqIDZzQ3t7HnxacG dSk482/F9adgEOPYA8mC549gRsjv06tfn33k9vqfxTffCyOwwfrzLjW4fspBH3hfP+3TMTuxddQ7 HnCSsRXTHipQQyDyfgkUc/5BlnuZ/4Nv1l2h/CfoFfNfyP+d/07c5E91wMnzANq0RWHUUlg4xzOL hsai3GtphyHYD3HM/ATmwQDWgS7betlTVhp3gX/K1dXMy5PepND5F1se5Pkd/h4FUUOI01NpoJyn /Kc6QBwhiEq8jfq90/+JC1B9iKBWgaip1aj1qDHUWnvsOvu4DI8NqMtRVwBhB6ARtcm+X5R7Lwzf vKYLDOX3btrDHYm9w+mRdN+o0T60Pz6aSA8Ym9dtsKCwrTt3zYKHY6zbDNOPfzAko0xDmLHIVCfm /vEW1DV4chBLx8E+wgSHivNBpx58HoXyeMz2Ypquo18HaCEOQTxL4Dj8cAQRo4sxKW7Nxi6zc8H5 Rn39UYDLeKPLT/cQydpqjWZbZt0lpAe4cya6qPVFy3EI62wdq7GvBXPPlfMXfJMbCfGr/CGos3su ZcIZPHsXdctGzByfyBh6phx2xEf37R4fxHL6vjX3LX799gFrvcfEJzWHyu7x1J50P0xswQt/N+s/ rORsog3VuKRNADICWl8bEzm5SZ/hR2n50OJpvFSzfmb+8Zg9Hmgt9eTak3Ts16Jk783ZTy6lV5DI 2UfDdL9z1l5CdkfO7gio/rf8qv92n+q/HYS/WA9kxA4eE9wG17M7keodMbp6x4xd6VR8ANzWQ8c/ cu/J1BoamDSvqflqyE7m7I6Qanfr6vNvMGGLuCbvOHG57NvPbvsm4pp938/RRbiYxJzgr64FQnZk KinlR2RqL6KeOagPg84Pt4KcC8n8XPA0VtIe68WmyFSPlZi5n3QcmfRFPdcDt7x0jcXOe9Q06rBt x1H7bTVyXvxwWZNVNdzFeZ+DtfQ+38nh6YRVUFrn4MklP77whqer7CMLT21Jx06FVHstF/Y8eCkA x3PxorXSEEYyYNunWqjqxfv7wbnyxCPk05ceNhyf91ZaPmnH/rCR7LU5u78qf30z/HgZPbPGa536 0Vv8M/xCZUH16qy3/Zjh31cXFO9PXuOtWlFQvOe8xrt8pRzvLD4Kq3Nz8fH8eque5uxDrWq9nWpS 7csrRP0t8v+He/4i/3+45f7g/zfOOfx/3/UofNezOPy/HgF2li82/5/kRoMb//8Y9SoO/xifn/8P 2nW/JHPDikH0E99sP4EjMX3r7V8icOWtP8euoRrGX2M9sb6Ayv9PsjCX+5P7eJuieqn7eE7/MNnF kMz/Tda2RObvJvs2KPcPk63XZf5usulSmf+b7ECJ6t/oU/1f4ap/h8L/DbuOufdFt/Wo/RZ4tlLm 88C1CpnvA/+9TLUb/erzYZX/Kzwyb986L/zqvm9qvzbZobpF4v+tUOT/+D6/qpD5P+LZL/P/WTzN kx9B933Lx9M09IRlvj8NsYCYx7ETTOH/Ml4KwPFcvDTXyvzfZJ/EVP5vslPVKv83WU+1zP9NdrRK 5v8m2xlU7ROasKnfU+XSQXQIErGeSosXAHxqAYNx3tQ9PjLam4IAxU5MoRGOWA707+ZvkTk8WHPZ x66nu55ZaJ+L8t+Iiu+TLFYif58s2Ke2LdSnVPyeZOcDnvtV2UL9Kj/er8s9x9teSLzZsOd4A4XE W6J8r07+6+9cXuvDZ/Xy95/JhmrVfhtaqtovRUT/lX8PaPXfdf5Dfu7vvhmBVRmYKOb//S3/ABpQ Tw0AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAACQAAHic7VpNbFtFEJ5dOz9+TuKfpknq0vIaIEoUESoiITgUhYY09NBQkgjELU6wiS3/ JLGLsYRE3aAcoIeqKheEClyqInGBCwc4WEhISEiABAdOFaWqQAgKUuGE6jCzP88/fUmfozTBqsf6 9Hbm7e7s7vzs2Ml33wZ++uDj0FWooSfBBaV1D7RWyBiCa8YP4Fay0vr6OolciPUmNRRNQxo/WTBh AlL4XIF8rStsSj3QYtmc/IF/Iz2kKF8fq+x77rPisbO5L1kXMV7tU89CAiJ16awkAzgj3dr3nIwZ RnSr9gQswykI485jeA4pPIcpxb3iaFUmRkTleTrRv5/WqgKJwTjqTcISnsM8xJ0Mr6LgFvTvQ0RV uw1xy8YvSgqdcHtM70FZoEIexHY7yDzQpMainYz/seLocxT/IvTv4fgPIf7cxfjvg3L863EtIPOA jvtKMkBc99CB8FWM8UAz5huddE1H8UPxS35ANR/dC5TTycZkf6+yP90HXcoPyCcCwgcB6E6gmNoL lBPKfrFPtenOuw9xAHEQcT9Q7AAcQvQjHkA8iHhoE59q+tr2E1f59yRm/ghk4LD4OKc+zL/ah4EB AACCAQAAgwEAAIQBAACFAQAAhgEAAIcBAACIAQAAiQEAAIoBAACLAQAAjAEAAI0BAACOAQAA/v// /5ABAACRAQAAkgEAAJMBAACUAQAAlQEAAJYBAACXAQAAmAEAAJkBAACaAQAAmwEAAJwBAACdAQAA ngEAAJ8BAACgAQAAoQEAAKIBAACjAQAApAEAAKUBAACmAQAA/v///6gBAACpAQAAqgEAAKsBAACs AQAArQEAAK4BAACvAQAAsAEAALEBAACyAQAAswEAALQBAAC1AQAAtgEAALcBAAC4AQAAuQEAALoB AAC7AQAAvAEAAL0BAAD+////vwEAAMABAADBAQAAwgEAAMMBAADEAQAAxQEAAMYBAADHAQAAyAEA AMkBAADKAQAAywEAAMwBAADNAQAAzgEAAM8BAADQAQAA0QEAANIBAAD+////1AEAANUBAADWAQAA 1wEAANgBAADZAQAA2gEAANsBAADcAQAA3QEAAN4BAADfAQAA4AEAAOEBAADiAQAA4wEAAOQBAADl AQAA5gEAAOcBAADoAQAA6QEAAOoBAAD+////7AEAAO0BAADuAQAA7wEAAPABAADxAQAA8gEAAPMB AAD0AQAA9QEAAPYBAAD3AQAA+AEAAPkBAAD6AQAA+wEAAPwBAAD9AQAA/gEAAP8BAAAAAgAAaD6n 4y601KHkDlS5n+2b9d7Qf7fivxfKcRxSbafxPwD2OaAZ/9tPuxX/pWb8/y/0GxiBb5IBRSaY/TUI AyV4nTLBw2hXev7FZHawo6mnGEaqy5BrqK39KQeciC2spDPpaNacWD4VzsbSKXN05LBIJU/PWDKR XjQzMgp/P/HJsrP1U07hcO2La6qeLrb3wuxMj2i7GHMZhpsxFlwdB5ePgRdbMUpaRnB1EIKrk4gh 4GtH8LlQ04MXTJRGEQlEGpGr7XFmEHhhEvgZnAN7V2FtGOQMYZt5NVwHOLBaJeANBDr5WqAfjPJI vnb+UHA1bumltZNeYLdprgs7Y7+Nx2v7fa/td6UHfniht7Hsd9TeZnfDXjsDWrlso+cVMqqdQqQR 2R1dS2OcGC+sICKIMGIBsaja84iEeEe0e/PZ66C417Uf3QCyJpD0IhZnn2IhON1C77ASdH2Ir7jI ubJS9HDdklUAtRina4haI6xPybxWvw4ObWMHqWIcaPVBSNUMVEkWsXWJOCwPL7XKipP6dMCJcHZx Nr+EGz7JSPe//HRJrvCcuLncHPyzsWQkY05FcuZ0OhlOwY/v3cxdRZjmP7mv+6J5eaPJGvZR4/3W d3xU2a5EwguL4flERNS6JB/z0ZSm1e+0l6pf0yItL7bZy8FtLx8DO/mc+/GQvfzVHnv57wGSp9JZ JW9X8vMBuW7Nv+unI49lND/lF+8tXu0zo+e13+ec236fc277feK8NfuU+i6zj/aSvqGM5tu7iR/M eBQf8bnkONA9bnSKFZq6x2WvW82sezzmFXNavN8gftLiz3qEDou/2SJnrPUhVpcPlasifZY/i7OM W3rWuqvX8XyQ+KMW/0wX8WFrZ2+30ozRRDpn7d1NPRYSuscSo9MZnByyeoyIaB2flHsx17e2F/H7 paNM0bxPGv0+2Xr+/9zK/1caMv//FohebOZ/+/wvcxlT447z2T1iXFzy7bxV9Cvz+z3V/IWWav4R Jnlpp+KtCjtxstNMPjmfTgDcCBl/LF4POsyxjL8m1n89bmP/qnmTXcZbG88LUL3fy6xf3DLDcc1/ 5SL+SNxQ3mcIDxVuBlK3X/w2hlEhfJpx3j+Tz2QjSciTntpv1G/8EgTn36anjoMTTRfJoys1QZWm 8i7vrMlZjtnwXWHz+XnhJaVhRWWcrMr5S+qZUM+XEfX95VESg/K/pGyF5Drr+81DjtmsT+PQfzLT AT8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACYAAHic7VpRTBxF GP5nb9njFlq4QzkoFRcU0qYtKVx9MGlNjHLEB1BLExLjA0e9S4+UOyhXyao1xBrS+NQn64Om+mR4 0Ijni0kfGpO+Fkx90CdLqKlGm5ioLzbcOf/s7LA7snd71wuI5SeT3W9m559//vnnn2+AleXw7U+W 9q2CJM9AAArFEGiOOkKLYoNmgDpeVygWi1gVoKW4KztKTkKW/uTAgEHI0Oc5MOVQKCmtNApsXRgb yk0rQq5bzXHnt5fNvi+uzN0gDdheb8fUi3AWkhWN6RSdRqRzPn76dNPyCNjjP0fnPwXT1I4JmKx4 /AgoBPeAHft++6X4cxBm4DwkqOfT1I4MXYcRjl735RWjivnjCsWI9a7Ssu7oX5CeIUAfAzTSgktW KO7K/0m2cv8bL/fcw/2/B9tDVl0N9j9xzsdPn+3e/49DTfc/UWHj3PUzfhds7H+7XxA28oCcA2TZ S79tAkYBIAy7OWEni594KSMV7z+MFzv+aiE1ns9DNb7N6TF/YR5BTo+cH/MBnvf2+Y+cDTkA5m55 /0doaQErpz4KeCYARGlpo6Wdln20dNCyn5bHaOkEKwYM/nyCP5+kzx5aemE3p2yV2Pc3ef232v+7 6709onD+9RJlfkmYhaPsx7+0VXH/QPkwWMEgZaSa8WspO3x8RVWgedScmsiepahJf/ODOxH4/uof c6u0GMZfc8ejqR7MDUeIdSYM6J+SIQUzxwGW0+8rdYU1puoykfX93a63eusjLOf87tA7XIcqDpbV S+18a7qEnZZewvV2qmH/9ka99cr2dqpR//ZeKOVXt71LWgX2tvn375JWgb1vV2Lvb3t929teib3x iNNeg8c30wuo91R6KjlrjCTnjJPZqUTGp72/1n3N9A5w3BIMs1tcjON5tciYUT/HIeUpYmHLjvlC dXbI88trb4RRxTGBf2l02pHX7tY77chrHwUQH+bYUMMh5zwM1d2+SG5xvInd8nrPn/nJ73rntVQz qjgi8A97EB8SeLXB3X4j5G5fD7rbl1lcnhDzcLcbqrt9kdRpFt4kLuR46/Cel7weQS1NnOPmAm68 Dlc5lv1JHige89prTaghI/CPuhvf19y4S0XWnp608QWWL4YEjrP4jU/a/uP9Bbb7E8r0Arp1hsi/ u0EOP5w+fS47m03ljMGZ84lcOpsxYn1H2VXg+VFRx64HNuiLwZ9PfzkDLgmDriwcgsjFOASaFGgg kYuT9PahoB8VWPsmyu+D46ut8N1YlL0HCAnoukoI/XiMd1Mu9WO3hUg3vZdgbNO2IVDeOUxVp4Ep Vd4/QMtB+rJwgtYk2DfxqvtnAL9WLg1IemJV6ukHyxE2jjHMVdiVxxzdA/Su1RAmzAKU4HgL3rh6 tSZ6s7LOfLyJXadvn9Ni0KvY3qB1Y8NvGmE4kTtzypxOAnxM5Py8Dfa7hHZT6jep9yt2PLvj31Dd 8b9I+lk+SQg85to/iyTv6r9IWln/sUmde1FnnraC1PJhM1gU9hrbNERRukfN2VxyCnpwn+OtuQve I3yO8O7dCMg5J+Axp5FnR17AZ2976opTD8rPQs9GDimnpxQvxDb77kc4tv/G9yq9zHdRh7wSxLYQ NfizAO7W/awVb4ohxX6zfgvK/iKo4HD41kfaeF2D+K5RGa9p/IKU74936Dfv3Hbn+3utqbAHfzXL 6etp18e99Xny17J6qZ3L10rY6cFf/dib8NbryV/92LtSyq8e/NWPvRP+/Sv4qx97v63EXs5f/dh7 uhJ7OX81q+Gv3vYK/mpK/NWU+Ksp8VezGv7qPT/BX02JvwrM+avAnJ+aEn8V2N0u+Otmdsvrfeur Vb/rLfirsIvzV4E5fxWY81eBOT8VmPNTMQ93u+CvYl6cv24WF3K8Jb3n5clfTYm/mhJ//Zc//fDX Uv7k/FX4g/NXgTn/FLhW/PU/eP6H0U/y+b+yVvn574f/bw1/9+Z/D8rfieNfiqqSh4//15T//QNi +kz+AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACIAAHic7VhdTFxVEJ5z Lz/dC5TdpWWBAl2gpa2kpLFPfajSIDZtLGKXRBOS2i3spmt29xZ2kaw2FsX0QRPtE2k0Qdroa6M1 RhJ9oNU+qvUB0/RFCBIfNVETG1Nw5vwsdy+7cJcSaAOzGe6Zc+acmXO/mTnncvcnz/S1L2pmwEbP gA7zCy4osvQxZE0JbuBj1De/sLBAXTrywhY9UXQaTPwlwQ8dEMfnAKTsobAsVUJhGvMCio8fRYRM iuHnrbqff/DSlx8P3WGlJLhUTL0IUQjlZdNKBmiMbGsy9pzM2Y68A5T9dtx/DC6gH+fgtbztezEj rO/TyZwa5LBsd0A/DEIQ33wE/YgjDp1Set3RW/Gvwn4tcisT7ULkh5b585KJSiAzn6nfbevzoFwM W3n/pNJ65v/k9SPfUP6XYXt4K/85bVT+n5T5r+Ztg6V1QD0NEGe8Inp/5SBK+NpE4RZtFKk7Hd3d KH/pPKB7HdX0bRJjwp/OAjq3yyT26iyg+u9FrgCRUzuBagKAD7kKuRq5AXmXnFOHz3rk3Tx2RV8j PptsMbZF60OarL9dWPlDkIBD/OecqrD+Mli8+zudd79oZR2nZN3P2q26OexvdP7vQVb5v1fqbNWB 9aM43Pvkr6EZZL//n6HqqnAPRcFBJqLhT8xtQv9pY5x9VU+xETf7QgkeGdTXU0/x4zeVfK2O5D6z VMpTlTR7MN5rxuOh3mRI6c3tJL0mnMcQcd0QMWy/O1IMnYr0DpgJM5z0d/QPBpMRM+4/3HqIh+Jz gXQfD08ltB6Gv4/c7LdH+hV+4ynQwN0diYUS/s7QkP+0Wcvjf/a2V96HrpzwQXegkrd1xnTDYN6R ADYxVbwjx1F5dD/yAWxcPgp6He9uB72cQQm2IpQRRg7ttEaZdtnTiGo0W+r2gva2H7wjYeQosok8 5GTZFlQM8snaO034HESOI9OCpmwTh2RfUrb7xJyNqv+1xXkYWYGs8bx2q24S+xnZEAtm1oMuX/ii vR6oHH55L8/9qEvKbzaSRnjAjCmNfY1cY2C5CvK45L/6f8g9lw9Kz/h4ezPkPx8zpUz9CdkfRh6Q YzHpXMRiWfr16CeAkN/fmbnOTJmQaXZzUTmeQhQhAiTC7D/NDaKEfMuDhmlaYyCVSIZicJGilm4t DfAen0B/3v3dCyKSmYxkUbMUGEJrLiXsj2qfFgtZ2Bp+aIkhDX/uQCp2zozCpWwp1Xms8wTYbIl1 27Qu/r5aUkpmln+pW4nGacfjB4VnLJsS0ltuGjmaXu9moZCF3zCv/GZZYp+yPQv+SzBefEdG8x6N XTqI7L+r494PrT16PXQHcYzeMm8f4KMmY5/d3+zVbFT7w7M6/Nuw49fdRkN2O48//mRD3f2ZtKkc GmgGmMDBq0U0hnVef0End2v5KNVyl6Za4hZQyLGkY4haraxK9pWk9Uq1s/p0I30xUFzUyDsDfUlM YusG7RgDbbsuvjhIpxROBZPnu1MXQgDTMnoK52cteBQs4gFvuI2aq795c95qxXsaY03c3/2pldab 8BhTudez4zvGbhGicGDFddHPXf/O5vYzMz7H2FSxY39/yb3uUn+Xw3/iKYH//TT+sTXBf7J5OfyH mx8F/+oq44wdL+stJl/8XT7jVu71Vo8/+vmqHafcty3n+KO/t3Ovu9TfhMuxv2dfycPflMexv9/l Xnepv74Kx/4G83m/P5Q69vf7fN7vgWarv5MZ5wit+6j137Lfc+fnnO73ASsqsZ53D9j1gozzLn1u ZNn/ndx27PsfZ19XWM+7cdZiWM+rcZbSreeVf0HZzXVeOdtfuX6D7y8i7YDm8ljlcv1kYeZ4qFjI 9v3n58fS/X+212pnnP28g+RgWp7jfh1Pqa+oke38KypqDimNZ/ldqjeq5GPb+Iy03FdEcnta/pBl jrfx2AlEsyCLO/sf8GpZegAAAAAAAAAAAAAAAAAAAAAAIgAAeJztV01sG0UUfjNrO/bmx4kDcWW1 YglS1B4SRQ1CFPEjKEmo1KTkR6oEHHDBVmzZcX5cIqsIHAUiARdQxZ+o0kCh3Chw5hAhcU0BcQBx SQkBcasESFSoMe/N7K53t/5Zu6EhyM8a776ZN2++mXlv9puvL3dsvP9Z5Ao45DIAMwAxAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAIA FwAAABkAAAD/////AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAvgEAACcFAAAA AAAAMgAzADMAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAgAAgH/////GgAAAP////8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAADTAQAAwgUAAAAAAAAyADYAMQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAACAP///////////////wAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAOsBAADzBQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA////////////////AAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQVBguxAAn6WOWQ3a AZr1uu1CoWC0Fxqyp2QcMvjLggaDMI3POcg5Q6GidIHX3HMFdb7ORf2abB6y2monx145t/AVayHF b8TUCUhBrKYxraICZzQ212PPTZ87sNwGxvhHcf5pmEEcpyBZ8/gh4LaYd9svrj+5Pv/HceVjMA/9 4ude9uH8Ke884H7+lNPnPPJdxXLdRZxs66UV7duwBEHmfUP2ttzK/M+/uzxD+S++KY38F7Jb+T+l 57+Bm1Q6B4w8bwK5RQFo5Pn/WQZhFk5DFDM/gXkwjefAqK495yortTrin3L1YzeGLqXW8Xda9vL4 Bn+ns9ujv3fh05r/xBGI6xNvs37/8QoAHUBnIEAnyDP1dixecHdmNM6V3ReGO6WoMoac3+4w/o0k npnLzGfiWW1w9nQ0m8hMawN9/SIUHp0w60R4GErfAPxx5PNZW5iFlpIUKypffrY7tDQCSpBBMwst JfYDnQebX75mWP7SBd+dDItXhTFFVdEqXbQ3PSkYuVgxjN3fOojlEL44nVc0XsSjazGOJYNlTtej WFJ60cB0AUuzN3oFgkb4/+btIl8AvhALyDjvnsjNZ2NpOPtGOH6WMuhOeNW8Pr/0a0jkWi+T627k nnF/5rrdI5hgK6j0eKgNM1Hp5LRa+0UrZVmAG2+SBXjF6OhCvPWxfXpds2nXwp/ma22UsT2+IER0 zkCZvIZvF7HkMb19XGY82bTASDQ7NZmbwc/BDMj5erc3BYbXaVDu4dA+kUufyqTwbAiqT77zcwi+ P//7whUsmvbnAq2BMV86Uw6rL7BrAu/BXDV/kbBaKO+PiXW7avH7Nm01HKrqF3E+VQmn9MtMv282 ucYLteAdCFjx5rdB9ys4HfqdTKRj89pobEEbz6Sj0y7x5tn5VtryRNLQmZ88Dpv6GS/pI6Ye4/b2 +0Q0ppMSl1aoD5dzvhvsJ58V1wYbYlJ3zh9ucv5jreRCSwZ0/bdmyrJoKhUzan4IUJ94Zk4z+rws 9kLLlMDi3GM+teV2j/PsmIdcXMioekapIE9egCJuBUrL6MOjx6x20if47gpS/8tJQz8i4vN+Uz8g x9T1NUXar5t6i7B/wNQjHmt/jIcma39zDnXt04XO+PHSawO+oMjX/iIum55nm0H7Pp5pM/ax1GpW OY2PE5JKp7Hb3SjKLfp+lhUm6XTdslv8/72bAe2QWsffadnL4/9b/D8M1e8ADf6/+/Jf4f8v6ob3 PhaG50/Y+L9yQJB317y+F1zfGCwWfNnfLRo7WvlyRzfQ0eaC/5fmH6ss5aPM6k1W+0pRbTn+fxRX +UdsfMLk/707wP/zitZcjv9/gmUDIfcppfn/1ar8P6Sq439t2rnRN5H4JTv/X2F3e9zx6Q+61A/L +3PyiRX2rdcd/0ecE5Vw2vdzhW35XeP9qBa8S6oV79p1KI930sk5y+O9xoZENG3lnPy9BN6L5f06 8QaVT4Xf9Rv8urkXlMcbVB4SHoZzhn4PWO8JwA/77fqiUvreUBsO5/xW2VjAeg9aZT1N8h5k6Kse e3uEy3tUPbyYcJRgqZdkfZGl0l+RpRYxV2epDf7f4P+V5R+d97SDAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAoAAB4nO1YXWgcVRQ+987kZ2c32c3E/JjWOqZSEktCaHywYsuWmK4WGkMSfRHEtE3o hG42yW6N+yBJGgm0iPRBCqLoKuhDwdIqIlEfgtWHQKl9UxBCii0WHyTgD4TSrOfMzN3c2ey2s7HU ptmznJ177tw7555zzzlzv7nyY9XiRxcarkIW7QUFVtI+KJX6GDIXQggg4PStpNNp6lKQ00XaUNQD MfwlwIBOGMbrGCSzQ+G2VAslmT2n/eeX7QiZs2/vl8dObv/qxY/Hf2AUU3OaiKkX4BgMFKRTJg04 I93ciT0vc55AfgiE/g60PwojuI5DMFSwfh0zQvan13mDzpU79nej5wcgDm3WzzvVo/2Ugyp4t78S eb9qt+lyS1r/isNl2F+O7AOy0c7x25EGxdzfiHQv8z/1+/yrlP8VUMz/+yX/xbr94K4DuUjUBpof BOsIkKkNVVDM/41InTAKx6EfM9/EPBjGOtDlSK95ykpjHfFPufqTl4EeqVD9d5s2sn5xfqfaTSWh xJHF+z/fe1/kP+U91YBqsGtqDdA7AaAOqDYBPIzcgLwFeStyKayvTtzp/FGk9RHDHVY0e0+y3920 hwfNw2OxeGwwYXSOHu9PmLFho721zYJ+z/Zm+oBeH0JobYe/dn8+KkeZPh1DHgclyMDP9GmTAkfj J5qsmOBQefEbZ+TpS7XwzJE6q60wpmgaDu/JmqhPN+Hj4sjNwGf2gPIIBrI+PZIZNgTOUMgIfKa8 UZ+OYGcFn6lqRO0zeuOaiSbQeGeiLeScqE935DCGT0WAn2gGqyxOeeIFdbaccvBynA5EO0qDeKKx 9wWcjLnJQ1BmSd9a28M4b+xNxhMDUZI0eAxOMeHnpd902LECE5TJLczO6CU8Hyh5sr9rX9fzdJ06 hGs5hmyVfHtp6LKpuNMeRo4hJzJLx2V4M3AT8JjlOD7Vj3wY+ajTdjk1D9Fei9rLHFl8Y+luBGjH gqmqdA+RmMI5ZctW6y5Vah8XLfsUSC3G8RFWq5XVO33+zLgAT5UYj1LFplhrcM6MVMnnsHUWeXEb wAEc6nfGBOBgf+JoX3IEzTjP7IicvGWv8LQVeSqHUJ8ZHYgbXQPjRk8s2j8Mj3M20YJsXFEmAE+0 IiLpnbJLC/P6bTS1OSnklq0kRzJy9xaSm5K2PlgR+lhB+piTAULvIo820BNMR8+C+qku611QXwqR q8whMX5njSwvqMs+a3xGvlBG94dMMf7rgFv+wlqxaWb7rTA7VjNZ+Ge+np7QYQr5n2qSRzJyjd+W fY7cySnKmuLNA2LEASveeuI5dpTjL9SbjB6KHYOJMHZcrNR2e/NwmFfU0SNa4kJ+p9Itv1xC8h5H L9xW76yhveLNI2f4k1X0iOtxIfeW23J2BOWx72lv9i2og1V2vbblwmo0/fXdkGv06vPvVKNP8n0h yyJnj0/yXbaFa2Irl4WfbdE+yWXhvXn/5ycmfVIu0r2nIv7b3PqL+G9z0/2B/379LoP/UGtfb63V 3gz4L6gEStaN/669qw9ey8aANxADFvHfg4D/bmJR/UW52/hvUjH0fPjvHPIiBn+rkhv/LTkROSmf pnPimJ8//HP8KrJh/D1OUerGfynWVyXjvxRrDck4LMXOBmX8Z6SFvny4Kbe+7NM78N1BGf8FlTc0 WW9QSfhkvAc8HJDloPJeiYz/gsoZVcZ7wF8vc8vb3fjvjjg2n9/caCfFnqqU8V+KnfDL+C/FTpXK +C/FjjA3/kux/W7858JH6ip6gNlqbeXSdd2jh1OsrULGe6i53C3vVWT8N3crn973y7Rwfr3ZHllm b/pk/LfM3lJl/LcaQTnsS3u3L6j84SvivyL+e1BobSa184ZaK2NNIccr3XLYqi17zP/6xZr+3F+s vWcDzT0X8fIN6e1t2ry3bzsf8O+tr47XI14yqkPXvvT2beo5XmN5dGdEyI4HI/+nB236F9aF0ZEA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAoAAB4nO0aS0xcVfTc+4bfA8rMUD6Flj6gqW342FhdkAZbqrVxUTSlsZvGOOA0zAzMKzCI E2MAaVmYmHSlbqytNrWmm1Y3mrig0UYTTa2NC90VU6KuNFEXFhk85917hzfDDDzooxGZMzl597z7 7rnnnHs+91649a3vzoVrNdOQBo+DBon5Isi3vWOIXBFegDz5LjE/P0+vNMT5HKwrOAom/mJgwCGI 4nMQ4umusCRUohcoXh7yj5vCQ6ZE91P2b6++2vj13yM3GPnUgWLlU89AHwRXNKcddOCM5ubS95yM aUbcDGr+J1D/fjiFcnRDeMXz+zEi7PZ0Ou6kfHKp/7No+SAMwR7r5xyqUYWVzk/xejdPtEsR5zL4 RSGQbQGKEAsQN4Gwb8KGOVj/4Gb8UwwuFf9nbz9/k+KfQt/t+FfgAQIAAAICAAD+//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////9kjMvxz6gGqtrnZAzGbDL+D8EA DEMALR9COaK4Dp2SesmRVQyc3wMLddfJ/DWIY0y01TjiQXkgW2z7sb8MUus7bgHAByJP5PLB+oT7 rz+rq3+q/rgBq5nfTVjP86s9PeUvygG0LLQ/o5pPewCq/xTflK5LQOwXaC9AuUDFP+WGchA5tQKo JgBUgcgJW+SzFp9bEbch1iFuh9XljFyecRcYroKmCx9Kr920hkdCPYPmkHkyZhwaGA7EQmbU2Nu6 x3KFJ7uS7yz3UETrXviz7aMBu5f1gX/CRBwBrYxBMfNPhMh1dI1ttfxv0+cvynp06/tK+CJQZbU1 xjRdx4+P4zCuhjE+6W8AGott/8Rh4K81I+swYgR5vbkLcTc2JtvxTSB9wm3WoIO21zSU3NjDGKM2 H8eaOh5FNBFjkh5EDCIGEHsQe2W7G7HP6kPBxkNypAFCsBMLgoGvlE/6GkAn8d0TjNZNxS6TuUCd 0ccxke/DAH4vj/qwoX3HydpbrV6K9CI+Yhw1+wNR2MHZaAuicUsbBawAxK8Fdzb0/J2JPPCIfq7g ynaaLRQ1giXiTV7TDuobDAZ6egPdfUH1ZV5jPY2NmjGjUL65YpCEhinpgh/9RJ8wFe+OMsnbULyv l2fm/ak3nXeHV/Am3Wb52JywwFnLqzwcvMdC/cEhozO4tL4g9WUg+IJ2Jp9YNJuUA3fml2EuFFED Mp/Ncq+VKwE+s8zOOG/oig/Fgv1gZc56eJ2pPHvsFz/sTMCo3barcqykM4m10SAzdHZ0Pq3swLLY QXmC2MVaNzrkU1arlVXLd8VcfVfCXyiEZr+0Ro3c81IlmMLWZcSpJqwchaJi0DclcCQQ6z0WP4Wa XOXCZj/98wpLrg/Hn7cr3t9t9sHoAXzxcaMezrY+Yl3u8RkKf9gVd8LvjSrdt5x/K76JImKxW/IF ux9lkjPizI+e0z7cQSxm4orev1nQGfw1k/x+Z/KD9mUtsWiJK7qtmOh2pU9iGX36nOlzh01yMU86 32x+5kz+cwXv1xOHw3EV17VWzghL+rz29i5yxVBY0d/UMRt9ruDXcuoPRxTd5rP4KTrvWhmz9Z/X WqtT+XVvYin0b0zQ6eu0Mj0X55WHHyIOB8OKfmsb0YEkfaMytb+lNLV/usCuJ2gXPXY9Qbtn5ajj kQzrniL3D+/+MTKNaBh/jVRUnWzMvC5jnirLX0MRRZt6Ku1jdjqfz3pT6YieSqvvpV1T/NKz4Jdw ulK/3Dvjh8xyptvV8DxmzdsSUfQHJUR/laSHrXzeLulLbEup/ftLbED2C7mM+WxyXazQr2eXK91+ MS1k6dsk57kHgm7JpH9Gv3Kq/wUrLzYn9dlfbtXYJP2O7Ff17H73D6r1X6of+7z6iJv1o65Bn1uL +oFyvvwg6gfKn8gmv/r7Tfr5rw7W9m85qz3H5c5/7oIb948qbxA4GGLdN6j7RzfAro97XDfG/Cs4 zzRS3Uk/05z+2b8oFy5/HlmA5c437tw/ZAcUlxc6Ndb/ENw8P2A9i+fODxvr/JC7P3pw90e9dxff HznJt0ut34O5/82+fun3v5/croRHz+Tuf9dUMFt9zdX/hX9p24jwL0fOF2EAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA= ------=_NextPart_01C59249.5AB2EAB0 Content-Location: file:///C:/0AA63DB2/NFGMcGill2_files/filelist.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C59249.5AB2EAB0--

1	A Contract-Based= Model for Directed Network Formation Shie Mannor Joint work with Ramesh Johari and John N. Tsitsiklis
2	The Context<= /font> Nodes/sensors configure themselves To establish connectivity To be able to deliver traffic (after possibly multiple hops) Prefer fewer links Dislike too much traffic through a node Centralized management versus = ; selfish/strategic behavior
3	The 3 Pillars Traffic: Prescribed traffic from i to j is B_ij Traffic must satisfy flow constraints Shortest path routing Bargaining: Connectivity cannot be forced Links are formed by contracts Directed links
4	The Basic Model<= /a> Graph G of n nodes Nodes wish to communicate between themselves Communication is expensive (power) Cost increases with amount of data (but not with distance ) Connectivity is imperative Number of hops is not important(?) Establishing a link may be costly
5	Relevance Applications: Storage Area Networks (SANs) and SSPs Internet/Peering for non-QoS traffic Privatized Mail (!) Part of the network formation sub-field includes: trade networks, knowledge sharing networks, buyer-seller networks. This work focuses on traffic and connectivity.
6	The Node’s= Dilemma
7	Cost Structure Every node suffers a cost: Terminating traffic is counted, but not originating traffic For simplicity all links cost the same (0) It is good to be a leaf Routing is part of the topology, we assume shortest path routing
8	Example Flow through 1:
9	Centralized Solu= tion One can try to solve the optimization problem for the whole network = and look for the “best” topology in terms of aggregate cost.= Best solution is a perfect graph
10	Social Approach Every node is altruistic, allowing each node to connect to it Impossible to guarantee minimality of network – will end up wi= th the perfect graph and many redundancies Specific nodes may suffer a lot of traffic without being compensated=
11	Negotiation Pro= cess Two nodes form a contract: Node i pays node j Node j receives traffic from node i and guarantees it reaches its destination if possible i compensates j for the excessive traffic sent through j j can decline to the contract, but for a high enough payment j should accept
12	Negotiation Pro= cess i offers $p_{ijto j, to form link ij} j demands $q_{ijfrom i, to allow the link} A link is formed if p_ij ≥ q_ij₌and p_ij > 0;= payment is p_ij A strategy s is a vector of offers & demands Given s, a graph G=3DG(s) is defined.
13	Payoff Given that graph G was generated by s The (static) game is now fully specified Note: it is not clear now if it is good to be a leaf
14	Routing Assumpt= ion Monotonicity: Satisfied by: Shortest path with equal splits Shortest path with pre-defined splits
15	Equilibrium= A set of bids and resulting graph is an equilibrium if: No node wishes to break an established link Offer: Demand: No pair of nodes w/o a link can reduce their total cost by forming a link
16	Questions:<= /font> Is there an equilibrium? Can a given graph be an equilibrium? What is the shape of the network at equilibrium for specific traffic structures? How good are they (w.r.t. social cost)?
17	Stabilizable Gr= aphs G is stabilizable if there exists s such that G(s)=3DG. Not all graphs are stabilizable
18	Connected graph= s Restrict attention to connected graphs: Esthetics Modeling B-connected graphs: Minimally B-connected: Every link is needed for G to be B-connected<= /li> Prop: G B-connected and stabilizable è= G Minimally B-connected
19	The Box Theorem= Given a graph, define: And When positive?
20	The Box Theorem= Let: Thm: G B-connected. s is link stable and G(s)=3DG iff
21	"The follo= wing are equivalent:" The following are equivalent: G is stabilizable G is minimally B-conne= cted and G is minimally B-conne= cted and
22	All to all traf= fic – many shapes of equilibria
23	Uniform All-to-= All Traffic
24	Concentrated Tr= affic Node 3 takes preference in routing Disconnecting 13:
25	MSDs= THM: If G is MSD then Lower bound is achieved only for a directed cycle Upper bound is achieved only for a bidirectional tree
26	"THM:"= ; THM: A stabilizable MSD exists iff = ; Furthermore, only the directed cycle = ; satisfies Step1: Ear decomposition Step2: Focus on A i₁ Step3: Do algebra
27	Uniform All-to-= All Traffic: Summary a: cost for each unreachable destination c: cost per unit flow a/c < n-1: no stabilizable MSD a/c =3D n-1: directed cycle is only stablizable MSD a/c ≥ 2n-3: all bi-directional trees are stabilizable a/c ≥ 2n²-2n: All MSDs are stabilizable; no other stabilizable graphs
28	Social Welfare properties Complete graph: n(n-1)c Best connected graph Bidirectional Star: 2(n-1)²c Best connected equilibrium Cycle: n² (n-1)c/2 Worst connected equilibrium Conclusion: Ratio Between worst and best is linear in n
29	Robustness<= /font> A notion of robustness - how sensitive results are to parameters. Measure as largest spread of accept/reject bids: For hierarchical graphs – most robust is a layered connection.=
30	Ongoing work Undirected links Not clear who’s paying who anymore Only trees can be stable Convergent dynamics via a potential function Bargaining games and sub-game perfect equilibria Massive simulations Efficiency loss Modeling flaw: the hub problem
31	Potentially Int= eresting User response Fixed link cost – cost sharing Routing as part of the strategy Delay for QoS traffic More complicated contracts Realistic applications And did we say dynamics?
32	A Contract-Base= d Model for Directed Network Formation Shie Mannor Joint work with Ramesh Johari and John N. Tsitsiklis