An Axiomatization of the Proportional Prenucleolus

Natalia Naumova

Authors

Natalia Naumova Saint Petersburg State University

Abstract

The proportional prenucleolus is deﬁned on the class of all positive TU games with ﬁnite sets of players. The set of axioms used by Sobolev (1975) for axiomatic justiﬁcation of the prenucleolus is modiﬁed. It is proved that the proportional prenucleolus is a unique value that satisﬁes 4 axioms: eﬃciency, anonymity, proportionality, and proportional DM consistency. The proof is a modiﬁcation of the proof of Sobolev’s theorem. For strictly increasing concave function U deﬁned on (0,+∞) with range equal to R¹, a generalization of the proportional prenucleolus is called U-prenucleolus. The axioms proportionality and proportional DM consistency are generalized for its justiﬁcation.

Keywords:

cooperative games, proportional nucleolus, prenucleolus, consistency

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