Article ID Journal Published Year Pages File Type
972213 Mathematical Social Sciences 2013 10 Pages PDF
Abstract

A game with restricted cooperation   is a triple (N,v,Ω)(N,v,Ω), where NN is a finite set of players, Ω⊂2NΩ⊂2N is a nonempty collection of feasible coalitions such that N∈ΩN∈Ω, and v:Ω→Rv:Ω→R is a characteristic function. The definition implies that if Ω=2NΩ=2N, then the game (N,v,Ω)=(N,v)(N,v,Ω)=(N,v) is the classical transferable utility (TU) cooperative game.The class of all games with restricted cooperation GrGr with an arbitrary universal set of players is considered. The prenucleolus and the prekernel for games with restricted cooperation are defined in the same way as the prenucleolus and the prekernel for classical TU games. Necessary and sufficient conditions for the collection ΩΩ to imply the single-valuedness of the prenucleolus are obtained. Axiomatic characterizations of the prenucleolus and of the prekernel for the class Gbr with a balanced collection of feasible coalitions ΩΩ are given.In the collection ΩΩ there may be identical players belonging to the same coalitions. In that case, the set of symmetric preimputations is defined as those where identical players have equal payoffs. The symmetric prenucleolus, being the nucleolus w.r.t. the set of symmetrical preimputations, is defined and characterized.

► Games with restricted cooperation are considered. ► The prenucleolus and the prekernel for such games are defined. ► Necessary and sufficient conditions for existence and single-valuedness of the prenucleolus are obtained. ► Axiomatic characterizations of the prenucleolus and of the prekernel for games with restricted cooperation are given.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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