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2博弈论MixedStrategies复旦大学王永钦.pptx


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2博弈论MixedStrategies复旦大学王永钦.pptx
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1Static(orSimultaneous-Move)pleteInformation-ES,Fudan2Fall,2007,FudanMatchingpenniesHeadisPlayer1’sbestresponsetoPlayer2’sstrategyTailTailisPlayer2’sbestresponsetoPlayer1’sstrategyTailTailisPlayer1’sbestresponsetoPlayer2’sstrategyHeadHeadisPlayer2’sbestresponsetoPlayer1’sstrategyHeadHence,NONashequilibrium-1,11,-11,-1-1,1Player1Player2TailHeadTailHead3Fall,2007,FudanSolvingmatchingpenniesRandomizeyourstrategiesPlayer1choosesHeadandTailwithprobabilitiesrand 1-r,respectively.Player2choosesHeadandTailwithprobabilitiesqand1-q,respectively.MixedStrategy:Specifiesthatanactualmovebechosenrandomlyfromthesetofpurestrategieswithsomespecificprobabilities.Player2HeadTailPlayer1Head-1,11,-1Tail1,-1-1,1q1-qr1-r4Fall,2007,FudanMixedstrategyAmixedstrategyofaplayerisaprobabilitydistributionoverplayer’s(pure)strategies.AmixedstrategyforChrisisaprobabilitydistribution(p,1-p),wherepistheprobabilityofplayingOpera,and1-pisthatprobabilityofplayingPrizeFight.Ifp=1thenChrisactuallyplaysOpera.Ifp=0thenChrisactuallyplaysPrizeFight.BattleofsexesPatOperaPrizeFightChrisOpera(p)2,10,0PrizeFight(1-p)0,01,25Fall,2007,FudanSolvingmatchingpenniesPlayer1’sexpectedpayoffsIfPlayer1choosesHead,-q+(1-q)=1-2qIfPlayer1choosesTail,q-(1-q)=2q-1Player2HeadTailPlayer1Head-1,11,-1Tail1,-1-1,1q1-q1-2q2q-1Expectedpayoffsr1-r6Fall,2007,Fudan1qr11/21/2SolvingmatchingpenniesPlayer1’sbestresponse B1(q):Forq<0.5,Head(r=1)Forq>0.5,Tail(r=0)Forq=0.5,indifferent(0r1)Player2HeadTailPlayer1Head-1,11,-1Tail1,-1-1,1q1-q1-2q2q-1Expectedpayoffsr1-r7Fall,2007,FudanSolvingmatchingpenniesPlayer2’sexpectedpayoffsIfPlayer2choosesHead,r-(1-r)=2r-1IfPlayer2choosesTail,-r+(1-r)=1-2rPlayer2HeadTailPlayer1Head-1,11,-1Tail1,-1-1,11-2q2q-1Expectedpayoffsr1-rq1-qExpectedpayoffs2r-11-2r8Fall,2007,FudanSolvingmatchingpenniesPlayer2’sbestresponse B2(r):Forr<0.5,Tail(q=0)Forr>0.5,Head(q=1)Forr=0.5,indifferent(0q1)Player2HeadTailPlayer1Head-1,11,-1Tail1,-1-1,1q1-q1-2q2q-1Expectedpayoffsr1-rExpectedpayoffs2r-11-2r1qr11/21/29Fall,2007,Fudan1qr 内容来自淘豆网www.taodocs.com转载请标明出处.