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时间:2018-02-11
《博弈论讲义perfect bayesian eqauilibrium》由会员上传分享,免费在线阅读,更多相关内容在工程资料-天天文库。
1、LectureXVII:DynamicGameswithIncompleteInformationMarkusM.MÄobiusMay1,2006²Osborne,chapter10²Gibbons,sections4.1and4.21IntroductionInthelasttwolecturesIintroducedtheideaofincompleteinformation.Weanalyzedsomeimportantsimultaneousmovegamessuchassealedbidauctionsandpublic
2、goods.Inpractice,almostalloftheinterestingmodelswithincompleteinforma-tionaredynamicgamesalso.Beforewetalkaboutthesegameswe'llneedanewsolutionconceptcalledPerfectBayesianEquilibrium.Intuitively,PBEistoextensiveformgameswithincompletegameswhatSPEistoextensiveformgamesw
3、ithcompleteinformation.Theconceptwedidlasttime,BNEisasimplythefamiliarNashequilibriumundertheHarsanyirepresentationofincompleteinformation.Inprinciple,wecouldusetheHarsanyirepresentationandSPEindynamicgamesofincompleteinformation.However,dynamicgameswithincompleteinfo
4、rmationtypi-callydon'thaveenoughsubgamestodoSPE.Therefore,many'non-credible'threatsarepossibleagainandwegettoomanyunreasonableSPE's.PBEallowssubgamereasoningatinformationsetswhicharenotsinglenodeswhereasSPEonlyappliesatsinglenodeinformationsetsofplayers(becauseonlytho
5、secanbepartofapropersubgame).ThefollowingexampleillustratessomeproblemswithSPE.11.1ExampleI-SPEOur¯rstexamplehasnoincompleteinformationatall.1LR222AB1313ItsuniqueSPEis(R,B).Thenextgamelooksformallythesame-however,SPEisthesameasNEbecausethegamehasnopropersubgames.1LRRR
6、2222ABAB13131313TheoldSPEsurvives-all(pR+(1¡p)RR;B)forallpisSPE.ButtherearesuddenlystrangeSPEsuchas(L;qA+(1¡q)B)forq¸1.Player2's22strategylookslikeannon-crediblethreatagain-butoutnotionofSPEcan'truleitout!Remember:SPEcanfailtoruleoutactionswhicharenotoptimalgivenany'b
7、eliefs'aboutuncertainty.Remark1Thisproblembecomesseverewithincompleteinformation:movesofNaturearenotobservedbyoneorbothplayers.Hencetheresultingexten-siveformgamewillhavenoorfewsubgames.Thisandtheaboveexampleillustratetheneedtoreplacetheconceptofa'subgame'withtheconce
8、ptofa'continuationgame'.1.2ExampleII:Spence'sJob-MarketSignallingThemostfamousexampleofdynamicgamewithincompleteinformationi
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