The prenucleolus for games with restricted cooperation

A game with a restricted cooperation is a triple (N, v,Ω), where N is a finite set of players, Ω ⊂ 2 , N ∈ Ω is a collection of feasible coalitions, v : Ω→ R is a characteristic function. The definition implies that if Ω = 2 , then the game (N, v,Ω) = (N, v) is the classical TU cooperative game. The class of all games with a restricted cooperation G with an arbitrary universal set of players is considered. The prenucleolus and the prekernel for games with a restricted cooperation are defined by the same way as the prenucleolus and the prekernel for classical TU games. Necessary and sufficient conditions to the collection Ω providing single-valuedness of the prenucleolus are obtained. Axiomatic characterizations of the prenucleolus and of the prekernel for the class G b with balanced collection of feasible coalitions Ω are given.