[博弈论书籍].game.theory,yuval peres,2004

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1、Stat155,YuvalPeresFall2004GametheoryContents1Introduction22Combinatorialgames72.1Somede¯nitions.........................72.2Thegameofnim,andBouton'ssolution............102.3Thesumofcombinatorialgames................142.4Staircasenimandotherexamples................182.5ThegameofGreenHackenbush......

2、...........202.6Wytho®'snim..........................213Two-personzero-sumgames233.1Someexamples..........................233.2Thetechniqueofdomination..................253.3Theuseofsymmetry.......................273.4vonNeumann'sminimaxtheorem................283.5Resistornetworksandtrollgames.....

3、...........313.6Hide-and-seekgames.......................333.7Generalhide-and-seekgames..................343.8Thebomberandsubmarinegame................373.9Afurtherexample........................384Generalsumgames394.1Someexamples..........................394.2Nashequilibrium.......................

4、..404.3Generalsumgameswithk¸2players.............444.4TheproofofNash'stheorem..................454.4.1Somemore¯xedpointtheorems............474.4.2Sperner'slemma.....................494.4.3ProofofBrouwer's¯xedpointtheorem........514.5Somefurtherexamples......................514.6Potentialgames......

5、....................521Gametheory25CoalitionsandShapleyvalue555.1TheShapleyvalueandtheglovemarket............555.2ProbabilisticinterpretationofShapleyvalue..........575.3Twomoreexamples.......................596Mechanismdesign611IntroductionInthiscourseongametheory,wewillbestudyingarangeofmathemati

6、calmodelsofcon°ictandcooperationbetweentwoormoreagents.Thecoursewillattemptanoverviewofabroadrangeofmodelsthatarestudiedingametheory,andthathavefoundapplicationin,forexample,economicsandevolutionarybiology.InthisIntroduction,weoutlinethecontentofthiscourse,oftengivingexamples.Oneclassofgamesthatweb

7、eginstudyingarecombinatorialgames.Anexampleofacombinatorialgameisthatofhex,whichisplayedonanhexagonalgridshapedasarhombus:thinkofalargerhombus-shapedregionthatistiledbyagridofsmallhexagons.Twoplayers,RandG,