Beyond Nash Bargaining Theory: The Nash Set

Roberto Serrano and Ken-Ichi Shimomura

July 1997

We extend Nash's bargaining theory to non-convex and coalitional problems. This paper investigates the implications of Nash-like axioms for bilateral problems and the properties of consistency and converse consistency over multilateral settings. The result is a characterization of the Nash set of NTU games, defined as the solution concept where each pair of players is splitting the gains from trade at a point where the Nash product of their utilities, subject to efficiency, is critical. The intersection of the Nash set and the core is also characterized with the same axioms for the class of games where the core is non-empty.

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