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1、Eco514／GameTheoryEco514—GameTheoryTheTremblingHand:Normal-FormAnalysisandExtensive-FormImplicationsMarcianoSiniscalchiJanuary17><0,2<0<0<0Introduction:InvarianceIntheirseminalcontribution,VonNeumannandMorgensternarguethatthenormalformofagamecontainsall“strategicallyrelevant”informa
2、tion.Thisview,notewell,doesnotinvalidateortrivializeextensive-formanalysis;rather,itleadsthosewhoembraceittobesuspiciousofextensive-formsolutionconceptswhichyielddifferentpredictionsindistinctextensivegamessharingthesamenormal(orreducednormal)form.Solutionconceptswhichdonotyielddif
3、ferentpredictionsforsuchgamesarecalledinvariant.Thesupposed“strategicsufficiencyofthenormalform”alsomotivatedthesearchfornormal-formsolutionconceptswhichexhibit“nice”propertiesineveryextensive-formas-sociatedwithagivennormal-formgame.ThemainproponentofthislineofresearchisJ.F.Merten
4、s.Inmyopinion,whetherornotthenormalformcontainsall“strategicallyrelevant”informationdependscruciallyonthesolutionconceptonewishestoapply.Thisisactuallyarathertrivialpoint,butIamafraiditwasoverlookedinthedebateonthesufficiencyofthenormalform.Forinstance,inordertocomputetheminmaxvalu
5、eofagame,oneonlyneedstolookatstrategiesandpayoffsassociatedwithstrategyprofiles;theinformationconveyedbytheextensiveformofthegame(ifsuchinformationisatallprovided)isirrelevantasfarastheminmaxvaluecalculationisconcerned.SinceVonNeumannandMorgensternweremostlyconcernedwithminmaxvalue
6、s,thenormalformwasindeedsufficientfortheirpurposes.TheargumentreadilyextendstoNashequilibriumanalysis.However,assoonasonewishestorestricttheattentiontosequentialequilibria,itisclearthatthenormalformisnotsufficienttocarryouttheanalysis.Quitesimply,theformalnotionof“normal-formgame”d
7、oesnotincludeaspecificationofinformationsets!Thispointismoresubtlethatitappears.Youwillrememberthat,givenanextensivegameΓanditsnormalformG,wedefined,foreachinformationsetI,thecollectionof1strategyprofileswhichreachI,S(I).Now,thelatterisanormal-formobject:itissimplyasetofstrategies.
8、Thekeypointisthat,inordert
