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Article

Ограниченное с-ядро в играх с ограниченной кооперацией

A game with  {\em{restricted cooperation}} is a triple (N,v,\Omega), where N is a finite set of players,
\Omega is  a non-empty collection oft feasible coalitions , and v a  characteristic function defined on \Omega.
U.Faigle (1989) obtained necessary and sufficient conditions for the non-emptiness of the core for games with restricted cooperation. Unlike the classical TU games the cores for games with restricted cooperation may be unbounded. Recently Grabisch and Sudh\"olter (2012) studied the core for games whose collections of feasible coalitions has  a hierarchical structure generated by a partial order relation of players.For this class of games they proposed a new concept -- the bounded core -- whose definition can be  extended to the general class of games with restricted cooperation as  the union of all bounded faces of the core. For this class of games  the bounded core can be empty even the core is not empty.
An axiomatization of the bounded core for the whole  class of games  with restricted cooperation is given with the help of axioms efficiency, boundedness, bilateral consistency, a weakening of converse consistency, and ordinality. Another axiomatization of the core is given for the subclass of games with non-empty cores that are bounded. The characterizing axioms are non-emptiness, covariance, boundedness, consistency, the reconfirmation property, superadditivity, and continuity.