The Modified Nucleolus: Properties and Axiomatizations

Peter SudhÃLter
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Peter SudhÃLter: Institute of Mathematical Economics-JMW-University of Bielefeld, Postfach 10 0131, 33501, Bielefeld, Germany
Authors registered in the RePEc Author Service: Peter Sudhölter

International Journal of Game Theory, 1997, vol. 26, issue 2, 147-182

Abstract: A new solution concept for cooperative transferable utility games is introduced, which is strongly related to the nucleolus and therefore called modified nucleolus. It takes into account both the "power", i.e. the worth, and the "blocking power" of a coalition, i.e. the amount which the coalition cannot be prevented from by the complement coalition. It can be shown that the modified nucleolus is reasonable, individually rational for weakly superadditive games, coincides with the prenucleolus for constant-sum games, and is contained in the core for convex games. Finally this paper proposes two axiomatizations of this solution concept on the set of games on an infinite universe of players which are similar to Sobolev's characterization of the prenucleolus.

Date: 1998-05-19
Note: Received: November 1994 Revised version: August 1995
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