rationalization and identification of discrete games with correlated types

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1、RATIONALIZATIONANDIDENTIFICATIONOFDISCRETEGAMESWITHCORRELATEDTYPESNIANQINGLIU?,QUANGVUONG†,ANDHAIQINGXU‡ABSTRACT.Thispaperstudiestherationalizationandidentificationofdiscretegameswhereplayershavecorrelatedprivateinformation/types.Allowingforcorrelatio

2、nacrosstypesiscrucial,forinstance,inmodelswithsocialinteractionsasitrepresentshomophily.Ourapproachisfullynonparametricinthejointdistributionoftypesandthestrategiceffectsinthepayoffs.First,undermonotonepureBayesianNashEquilibriumstrategy,wechar-acteri

3、zealltherestrictionsifanyonthedistributionofplayers’choicesimposedbythegame-theoreticmodelaswellasrestrictionsassociatedwiththreeassumptionsfrequentlyusedintheempiricalanalysisofdiscretegames.Namely,weconsideradditiveseparabilityofprivateinformation,e

4、xogeneityofpayoffshiftersrelativetoprivateinformation,andmutualindependenceofprivateinformationgivenpayoffshifters.Second,westudythenonparametricidentificationofthepayofffunctionsandtypesdistribution.Inparticular,weshowthatthemodelwithexogenouspayoffsh

5、iftersandseparableprivateinformationisfullyidentifieduptoasinglelocation–scalenormalizationundersomeexclusionrestrictionsandrankconditions.Third,wediscusspartialidentification,multi–dimensionaltypesandmultipleequilibria.Lastly,webrieflypointouttheimplica

6、tionsofourresultsformodeltestingandestimation.Keywords:Rationalization,Identification,DiscreteGame,SocialInteractionsJEL:C14,C18,C31,C35,C52,andZ13Date:October,2013.WethankLaurentMathevet,BernardSalanie,StevenStern,ElieTamer,NeilWallaceandNeseYildizfo

7、rusefulcomments.WealsothankseminarparticipantsatPennsylvaniaStateUniversity,TexasMetricsCamp2013,TexasA&MUniversity,UniversityofChicago,BrownUniversity,UniversityofTexasatAustin,ColumbiaUni-versity,RiceUniversity,NewYorkUniversity,theNorthAmericanSumm

8、erMeetingatUniversityofSouthernCalifornia,andthe2013AsianMeetingoftheEconometricSocietyatNationalUniversityofSingapore.ThesecondandthirdauthorsrespectivelyacknowledgefinancialsupportsfromtheNationalScienceFoundationthroughgrantSES1148149andtheS