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1序贯博弈和同时博弈的结合CombiningSequentialandSimultaneousMoves第6章Chapter6Slide2序贯博弈和同时博弈的结合CombiningSequentialandSimultaneousMoves收益表（策略形式）Payofftables(Strategicform)纳什均衡Nashequilibrium纯粹同时博弈PurelySimultaneous-movegames博弈树（扩展形式）GameTrees(Extensiveform)反转均衡Rollbackequilibrium纯粹序贯博弈PurelySequential-movegames分析技术TechniquesofAnalysis概念Concepts博弈类型GameTypeSlide3序贯博弈和同时博弈的结合CombiningSequentialandSimultaneousMoves在现实中，许多策略环境包含了这两种相互作用的成分。Inreality,manystrategicsituationscontainelementsofbothtypesofinteraction.而且，我们还可以使用扩展形式和策略形式分析任何一种博弈（可以交叉使用）。Also,wecanuseeitherextensiveformorstrategicformforanytypeofgame.Slide4内容提要Outline兼具同时和序贯行动的博弈Gameswithbothsimultaneousandsequentialmoves改变博弈中的行动顺序Changingtheorderofmovesinagame改变分析方法ChangingthemethodofanalysisSlide5兼具同时和序贯行动的博弈GameswithBothSimultaneousandSequentialMoves典型的例子一般都是博弈者在持续的一段时间内相互作用。Themostobviousexamplesarethosebetweenplayersoveranextendedperiodoftime.这样的博弈是同时利用博弈树和反转，以及收益表和纳什均衡的工具来分析的。Suchgamesareanalyzedbycombingthetoolsoftreesandrollback,andpayofftablesandNashEquilibrium.Slide6兼具序贯和同时行动的一个两阶段博弈ATwo-stageGameCombiningSequentialandSimultaneousMoves有两个可能成为电信巨头的企业：C和G。There’retwowould-betelecomgiants,CrossTalkandGlobeDialog.每个企业都需要同时选择是否投资100亿以购置光纤网。Eachcanchoosewhethertoinvest$10billioninthepurchaseofafiberopticnetwork,simultaneously.如果一个企业投资了而另一个没有，投资的企业需要确定其电信服务的定价。Ifoneinvestsandtheotherdoesnot,thentheinvestorhastomakeapricingdecisionforitstelecomservice.如果两个企业都投了，那么他们的定价选择成为一个第二阶段的同时博弈。Ifbothinvest,thentheirpricingchoicesbecomeasecondsimultaneous-movegame.2Slide7兼具序贯和同时行动的一个两阶段博弈ATwo-stageGameCombiningSequentialandSimultaneousMoves,0Invest0,0,0Don’tCROSS-TALKInvestDon’tGLOBEDIALOG(billiondollars)Secondstage:GlobalDialog’spricingdecisionGLOBAL-DIALOG146HighLowSecondstage:CrossTalk’spricingdecisionCROSS-TALK146HighLow-2,-26,-10Low-10,62,2HighCROSS-TALKLowHighGLOBEDIALOGSecondstage:pricinggameFirststage:InvestmentGameSlide8兼具序贯和同时行动的一个两阶段博弈ATwo-stageGameCombiningSequentialandSimultaneousMoves-2,-214,0Invest0,140,0Don’tCROSS-TALKInvestDon’tGLOBEDIALOG第一阶段投资博弈（代入从第二阶段均衡中得出的反转收益后）StageoneInvestmentGame(AfterSubstitutingRolled-BackPayoffsfromtheEquilibriumoftheSecondStage)TwoNashEquilibria:AChickenGameSlide9子博弈Subgames一个子博弈是整个博弈的一部分，它自身就构成一个完备博弈，具有完整的结构：参与者、策略和收益。Asubgameisapartofafullgame,whichisalsoafull-fledgedgameinitsownright,withafullyspecifiedstructureofplayers,strategies,andpayoffs.Slide10子博弈Subgames更一般的，一个子博弈是多次行动博弈的一部分，它开始于原博弈的某一个节点。Moregenerally,asubgameisthepartofamultimovegamethatbeginataparticularnodeoftheoriginalgame.子博弈的博弈树就是整个博弈的博弈树中以这一节点为初始点的完整部分。Thetreeforasubgameisthenjustthewholepartofthetreeforthefullgamethattakesthisnodeasitsroot,orinitial,node.一个多次行动博弈具有的子博弈数目等于其决策点数目。Amultimovegamehasasmanysubgamesasithasdecisionnodes.问题：在刚才的两阶段博弈中，共有多少个子博弈？Howmanysubgamesdowehaveintheprevioustwo-stagegame?Slide11多阶段博弈的构成：例子ConfigurationsofMultistageGames:Examples-2,-26,-10Low-10,62,2HighCROSS-TALKLowHighGLOBEDIALOGGLOBAL-DIALOG0,140,6HighLow假设G事先已经投了100亿了SupposeGlobalDialoghasalreadymadethe$10billioninvestment……CROSS-TALKInvestDon’t(C,G)Slide12多阶段博弈的构成：例子ConfigurationsofMultistageGames:Examples3进攻阵形21防守阵形中国女足进攻阵形防守阵形德国女足德国女足12反应不反应中国女足不变阵变阵-1第一阶段为同时、第二阶段为序贯：零和博弈Simultaneous-moveFirstStageFollowedbySequentialMoves:AZero-SumGame背景：在2004年奥运会上，中国女足以0比8惨败给德国。3Slide13多阶段博弈的构成：例子ConfigurationsofMultistageGames:Examples13进攻阵形21防守阵形中国女足进攻阵形防守阵形德国女足NopurestrategyNashequilibrium.ItturnsoutourChineseteamshouldchoosetheattacklineupwithprobability1/3.(ShowninCh7)Slide14改变博弈中的行动顺序ChangingtheOrderofMovesinaGame序贯博弈可以变成同时的，如果参与者在做出自己的选择时，不能观察到对手的行动。Sequential-movegamesbecomesimultaneousiftheplayerscannotobservemovesmadebytheirrivalsbeforemakingtheirownchoices.这样，我们就得去寻找纳什均衡而非反转均衡。Inthatcase,wewouldanalyzethegamebysearchingforaNashequilibriumratherthanforarollbackequilibrium.Slide15改变博弈中的行动顺序ChangingtheOrderofMovesinaGame同时博弈也可以变成序贯的，如果某一参与者能够在做出自己选择前观察到其他人的行动。Asimultaneous-movegamecouldbecomesequentialifoneplayerwereabletoobservetheother’smovebeforechoosingherown.博弈规则的任何改变也能改变博弈结果。Anychangestotherulesofthegamecanalsochangeitsoutcome.Slide16变同时博弈为序贯博弈ChangingSimultaneous-MoveGamesintoSequential-MoveGames结果不变Nochangeinoutcome先行者优势First-moveradvantage后行者优势Second-moveradvantage双方都更好BothPlayersmaybebetterSlide17结果不变NoChangeinOutcome某些博弈，无论是同时的，还是序贯的，也无论序贯博弈中行动顺序如何，结果都不变。Certaingameshavethesameoutcomesintheequilibriumofbothsimultaneousandsequentialversionsandregardlessoftheorderofplayinthesequentialgame.这一结果通常产生在所有博弈者都具有优势策略时。Thisresultgenerallyarisesonlywhenbothorallplayershavedominantstrategies.Slide18例：囚徒困境的三个版本ThreeVersionsofthePrisoners’DilemmaGame3yr,3yr25yr,1yrDeny(Cooperate)1yr,25yr10yr,10yrConfess(Defect)HUSBANDDeny(Cooperate)Confess(Defect)WIFEHUSBANDConfessConfessConfessDenyDenyDeny10,1025,11,253,3WIFEWIFEHUSBAND,WIFEWIFEConfessConfessConfessDenyDenyDeny10,1025,11,253,3HUSBANDHUSBANDWIFE,HUSBAND(a)Simultaneousplay(b)Sequentialplay:Husbandmovesfirst(c)Sequentialplay:WifemovesfirstNotice:Lowernumbersanbetterthanhigherones.4Slide19先行者优势First-MoverAdvantage先行者优势可能产生在博弈规则从同时行动变为顺序