[博弈论书籍].game.theory,alive,yuval peres

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1、GameTheory,AliveYuvalPeresiTheauthorwouldliketocordiallythankAlanHammond,forscribingthe¯rstdraft;GaborPete,YunLongandPeterRalphforscribingtherevisions;YelenaShvetsforpicturesandediting;RanjitSamraofrojayso-riginalart.comforthelemon¯gure.ThanksalsotoItamarLandauandSithparranVanniase

2、garamforcorrec-tionstoanearlierversionandmakingvaluablesuggestions.ThesupportoftheNSFVIGREgranttotheDepartmentofStatisticsattheUniversityofCalifornia,Berkeley,andNSFgrantsDMS-0244479andDMS-0104073isacknowledged.Contents1Introductionpage12Combinatorialgames62.1ImpartialGames72.1.1Ni

3、mandBouton'sSolution122.1.2OtherImpartialGames162.1.3ImpartialGamesandtheSprague-GrundyTheorem232.2PartisanGames292.2.1TheGameofHex322.2.2TopologyandHex:aPathofArrows*342.2.3HexandY352.2.4MoreGeneralBoards*372.2.5AlternativeRepresentationofHex382.2.6OtherPartisanGamesPlayedonGraphs

4、403Two-personzero-sumgames483.1Preliminaries483.2VonNeumann'sMinimaxTheorem523.3TheTechniqueofDomination563.4TheUseofSymmetry583.5Resistornetworksandtrollgames603.6Hide-and-seekgames623.7Generalhide-and-seekgames653.8Thebomberandbattleshipgame674Generalsumgames744.1Someexamples744.

5、2Nashequilibrium764.3CorrelatedEquilibria804.4Generalsumgameswithmorethantwoplayers83iiContentsiii4.5TheproofofNash'stheorem854.6FixedPointTheorems*874.6.1EasierFixedPointTheorems874.6.2Sperner'slemma904.6.3Brouwer'sFixedPointTheorem924.7EvolutionaryGameTheory934.7.1HawksandDoves94

6、4.7.2EvolutionarilyStableStrategies964.8Signalingandasymmetricinformation1014.8.1Examplesofsignaling(andnot)1024.8.2Thecollapsingusedcarmarket1044.9Somefurtherexamples1054.10Potentialgames1065Random-turnandauctioned-turngames1145.1Random-turngamesde¯ned1145.2Random-turnselectiongam

7、es1155.2.1Hex1155.2.2Bridg-It1165.2.3Surround1175.2.4Full-boardTic-Tac-Toe1175.2.5RecursiveMajority1185.2.6Teamcaptains1185.3Optimalstrategyforrandom-turnselectiongames1195.4Win-or-loseselectiongames1215.4.1Lengthofplayforrandom-turnRecursiveMajority1225.5Richmangames1235.6Addition

8、alnotesonRandom-turnHex126