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

Hans Keiding

Annals of Operations Research, 1998, vol. 84, issue 0, 238 pages

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

Date: 1998
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DOI: 10.1023/A:1018992904921

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