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On the structure of the set of Nash equilibriaof weakly nondegenerate bimatrix games

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  • Hans Keiding

Abstract

In two-person games where each player has a finite number of pure strategies, the set of Nash equilibria is a finite set when a certain nondegeneracy condition is satisfied. Recent investigations have shown that for n × n games, the cardinality of this finite set is bounded from above by a functionφ(n) with 2 n − 1 ≤ φ(n) ≤ (27/4) n/2 − 1, where n is the maximal number of pure strategies of any player. In the present paper, we generalize this result to a class of games which may not satisfy the nondegeneracy condition. The set of Nash equilibria may be infinite; it is shown that it consists of no more than φ(n) arc-connected components. Copyright Kluwer Academic Publishers 1998

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  • Hans Keiding, 1998. "On the structure of the set of Nash equilibriaof weakly nondegenerate bimatrix games," Annals of Operations Research, Springer, vol. 84(0), pages 231-238, December.
    • Handle: RePEc:spr:annopr:v:84:y:1998:i:0:p:231-238:10.1023/a:1018992904921
    DOI: 10.1023/A:1018992904921
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    Cited by:

    1. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.

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