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Article

Пред n-ядра в играх с ограниченной кооперацией

Translator: И. В. Кацев

A cooperative game with restricted cooperation is a triple (N,v,Omega), where N is a finite set of players, Omega is a collection of  feasible} coalitions, v:Omega -->R is a characteristic function. The definition implies that if Omega=2^N, then the game (N,v,Omega)=(N,v) is a classical cooperative game with transferable utilities (TU). The class of all games with restricted cooperation  with an arbitrary {\it universal} set of players is considered. The prenucleolus for the class is defined in the same way as for classical TU games. Necessary and sufficient conditions on a collection Omega providing existence and singlevaluedness of the prenucleoli for the class into consideration are found.  Axiomatic characterizations of the prenucleolus for games with two-type collections Omega generated by coalitional structures