合作博弈论 Cooperative Game Theory

asekaran,extendtwopersongametheorytoconsidernpersongamesforn≥3,thereislittlediffnceofNashequilibriumfollowsfromsimilarargumentsandallthediffireisanewphenomenonherethatmustbetakenintoaccount:—sofplayerscouldforma"cartel"srequireshavingbindingcontracts,usingcorrelatedmixedstrategies,andtransferableutility(sothatthegaincouldbesharedbetweenthecolludersinsomewaythatallagreeto).Themainstudyhereistomodelthecoalitionformation,presentation:CharacteristicFunctionFormsLetN={1,2,...,n}finition1Byacharacteristicfunctionofann-persongamewemeanafunctionvthatassignsavaluetoeachsubsetofplayers;:2N→kofv(S)asthepayofftothesubsetSofNifitactsinunison;sometimesitisalsoassumedthatthisismaximinpayoffinthatwealsothinkallofN−Sactinunison(againstS).v(S)gofromgamesinextensiveformstonormalforms,weabstractsomedetailsandonlylookatstrategiestoobtaina(mixed)equilibrium(forwhichwedonotneedthedetailsthathavebeenabstractedaway).Similarly,1

innpersoncooperativegameswherethestudyfocusesonstablecoalitionformations,weabplicitlyassumedthatacoalitionScandistributeitsvaluev(S)hesearealsocalledtransferableutilitygames(TUgamesforshort).nerallyassumethatv({φ})=0;v(S)≥0∀S⊆es/SolutionsAnoutcomeofagameincharacteristicformcon-sistsof:(i)ApartitionofNintocoalitions,calledacoalitionstructure,and(ii)apayoffvector,tionstructureCSoverNisanonemptycollectionofnonemptysubsetsCS={S1,S2,...,Sk}satisfyingtherelations:∪ki=1Si=N;Si∩Sj=φifi=jThesetofallcoalitionstructures