An admissible set occurring in various bargaining situations

Ehud Kalai*, David Schmeidler

*Corresponding author for this work

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

Given a set of alternatives S and a binary relation M on S the admissible set of the pair (S, M) is defined to be the set of maximal elements with respect to the transitive closure of M. It is shown that existing solutions in game theory and mathematical economics are special cases of this concept (they are admissible sets of a natural S and M). These include the core of an n-person cooperative game, Nash equilibria of a noncooperative game, and the max-min solution of a two-person zero sum game. The competitive equilibrium prices of a finite exchange economy are always contained in its admissible set. Special general properties of the admissible set are discussed. These include existence, stability, and a stochastic dynamic process which leads to outcomes in the admissible set with high probability.

Original languageEnglish (US)
Pages (from-to)402-411
Number of pages10
JournalJournal of Economic Theory
Volume14
Issue number2
DOIs
StatePublished - Apr 1977

ASJC Scopus subject areas

  • Economics and Econometrics

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