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1、Chapter1完全信息静态博弈StaticGamesofCompleteInformationInthischapterweconsidergamesofthefollowingsimpleform:first,theplayerssimultaneouslychooseactions;then,theplayersreceivepayoffsthatdependonthecombinationofactionsjustchosen.Withintheclassofsuchstatic(orsimultaneous-move)game
2、s,werestrictattentiontogamesofcompleteinformation.Thatiseachplayer’spayofffunction(thefunctionthatdeterminestheplayerspayofffromthecombinationofactionschosenbytheplayers)iscommonknowledgeamongalltheplayers.教材P21一、Normal-FormRepresentationofGamesandNashEquilibrium(一)Norma
3、l-FormRepresentationofGamesInthenormal-formrepresentationofagame,eachplayersimultaneouslychoosesastrategy,andthecombinationofstrategieschosenbytheplayersdeterminesapayoffforeachplayer.Weillustratethenormal-formrepresentationwithaclassicalexample—Theprisoners’Dilemma.＊Two
4、suspectsarearrestedandchargedwithacrime.Thepolicelacksufficientevidencetoconvictthesuspects,unlessatleastoneconfesses.Thepoliceholdthesuspectsinseparatecellsandexplaintheconsequencesthatwillfollowfromtheactionstheycouldtake.Ifneitherconfessesthenbothwillbeconvictedofamin
5、oroffenseandsentencedtooneyearinjail.Ifbothconfessthenbothwillbesentencedtojailfiveyears.Finally,ifoneconfessesbuttheotherdoesnot,thentheconfessorwillbereleasedimmediatelybuttheotherwillbesentencedtoeightyearsinjail—fiveforthecrimeandafurtherthreeforobstructingjustice(干扰
6、司法)。囚徒２招认 沉默招认 –5,-50,-8囚徒１沉默-8,0-1,-1囚徒的困境Wenowturntothegeneralcase.Thenormal-formrepresentationofagamespecifies:(1)theplayersinthegame;(2)thestrategiesavailabletoeachplayer;(3)thepayoffreceivedbyeachplayerforeachcombinationofstrategiesthatcouldbechosenbytheplayers.Def
7、inition:Thenormal-formrepresentationofan-n-playergamespecifiestheplayers’strategyspacesS1,…,Snandtheirpayofffunctionsu1,…,un.WedenotethisgamebyG={S1,…,Sn;u1,…,un}.教材 Ｐ22＊理解完全信息静态博弈时要注意事项１Althoughwestatedthatinanormal-formgametheplayerschoosetheirstrategiessimultaneously
8、,thisdoesnotimplythatthepartiesnecessarilyactsimultaneously:itsufficesthateachchoosehisorheractionwitho
