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1、SelectionbyCommitteeThomasS.FergusonDepartmentofMathematicsUniversityofCaliforniaatLosAngelesLosAngeles,CA90095-1361,USAtom@math.ucla.eduAbstractThemany-playergameofsellinganasset,introducedbySakaguchiandextendedtomonotonevotingproceduresbyYasuda,NakagamiandKurano,isreviewed.Conditionsfor
2、auniqueequilibriumamongstationarythresholdstrategiesaregiven.Keywords.sellinganassetgame,monotonevotingprocedures,thresholdstrategies.AMSSubjectClassifications.60G40,90G39,90D45.1IntroductionThetheoryofcommitteedecisionsisnotwelldeveloped.Withoutsometreat-mentofcommitteedecisionproblems,th
3、eBayesianphilosophicalviewpointisnotcomplete.Wereviewananalysisoftheproblemofselectionofacandidatebyacommittee.Thisisessentiallyagame-theoreticversionwithmanyplayersoftheproblemofsellinganasset.Acommitteeischargedwiththedutyofselect-ingacandidateforaposition.Eachmemberofthecommitteehashis
4、ownwayofviewingacandidate’sworth,whichmayberelatedorsomewhatopposedtotheviewpointsoftheothermembers.Candidatesappearsequentially.ThestudyofthisproblemwasinitiatedbySakaguchi[2]andcontinuedingreaterdepthinSakaguchi[3,4],Kuranoetal.[1],Yasudaetal.[6]andSzajowskiandYasuda[5].Herewelookatthep
5、roblemofuniquenessofperfectequilibria.Thisproblemarisesinthesimplestofsettings.ItmaybeconsideredasastudyoftheequilibriumequationsofSakaguchi.2TheProblemLetmdenotethenumberofcommitteemembers,referredtobelowasplayers,andletMdenotethesetofallplayersM={1,...,m}.Theplayerssequen-tiallyobservei
6、.i.d.m-dimensionalvectors,X1,X2,...,fromaknowndistribu-tionF(x)withfinitesecondmoments,E(
7、X
8、2)<∞.Aftereachobservation,204T.S.Fergusontheplayersvoteonwhetherornottoacceptthepresentobservation(stop)ortocontinueobserving.Theplayershavepossiblydifferingcostsofobservation.Letc=(c1,...,cm)denote
9、them-vectorofcosts,withplayeripayingciforeachobservation.Ifatstagen,theplayersvotetoacceptthepresentobservation,Xn=(Xn1,...,Xnm),thenthepayofftoplayeriisXni−ncifori=1,...,m.Thevotingdecisionismadeaccordingtotherulesofasimplegame.Acoalitionisasubsetoftheplayers.LetC=
