, Volume 6, Issue 4, pp 249-255

A generalization of theKohlberg criterion

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Abstract

TheKohlberg criterion, which characterizes the nucleolus of a game (over the set of all imputations) in terms of balanced collections, is here extended to the sets of payoff vectors for various coalition structures. It is shown that one generalization yields a necessary condition; another yields a sufficient condition. A necessary and sufficient condition — which is unfortunately somewhat difficult to verify — is also given.

Research supportued by National Science Foundation Grant MCS 76-23865.