TY - JOUR

T1 - An admissible set occurring in various bargaining situations

AU - Kalai, Ehud

AU - Schmeidler, David

PY - 1977/4

Y1 - 1977/4

N2 - 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.

AB - 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.

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U2 - 10.1016/0022-0531(77)90139-9

DO - 10.1016/0022-0531(77)90139-9

M3 - Article

AN - SCOPUS:0001646788

VL - 14

SP - 402

EP - 411

JO - Journal of Economic Theory

JF - Journal of Economic Theory

SN - 0022-0531

IS - 2

ER -