Non classical approaches to cooperative games

Abstract

In thisthesis,ouraimisthreefoldandconsistsinexploringthreenonclassicalapproaches of cooperativegames.Inacooperativegamewithtransferableutilities,eachcoalitionthat is formedisendowedwithapre-determinedworth.Thisisnotalwaysthecaseasshownin our investigations.Firstly,weassumethatthepayoffofacoalitiondependsonthechoice of itsmembersbetweentwoormoreavailablealternatives.Bysodoing,weintroduce the classofmulti-cooperativegameswithtransferableutilities(MTU-games) byassuming that, insteadofasinglegame,playersareofferedtwoormoreTU-games.ForMTU-games, wedefinesomecoreconcepts;andthenweprovenecessaryandsufficientconditionsof the non-emptinessforthecorrespondingcores.Secondly,weconsidercooperativegames with possiblynon-monetarysharingissuesbyassumingthateachoutcomeofcooperation is arawmaterialeachshareofwhichismadeprofitablebyplayersintheirownway. Forthesegames,called cooperativegameswithlocalutilitiesfunctions(LUF-games), twocoreconceptsareintroduced.For core sharingvectors, nocoalitionexistssuchthat all itsmembersarebetteroffby stayingoutofthegrandcoalition; whileforstrongcore sharing vectors,anydeviationthatisprofitableforsomemembersofacoalitionalsomakes some othersinthatcoalitionworseoff.Theresultsobtainedincludeageneralizationof the Shapley-Bondarevatheoremtolinearutilityfunctionswithpossiblydistinctrates. Thirdly andfinally,wefollow Charnes andGranot (1973,1976) oncooperativegames when payoffsofcoalitionsarerandomvariables;theso-calledchance-constrainedgames. On thisstrandoftheliterature,weencompasstheabsenceofasingle-valuedsolution bydefiningatwo-stagevalueasanex-anteagreementamongplayers.Insupportofthe tractabilityofthenewlyintroducedvaluecalled equal-surplusShapleyvalue, asimpleand compact formulaaswellasaxiomaticsolutionsareestablished.