On the Set of Proper Equilibria of a Bimatrix Game

Mathijs Jansen

International Journal of Game Theory, 1993, vol. 22, issue 2, 97-106

Abstract: In this paper it is proved that the set of proper equilibria of a bimatrix game is the finite union of polytopes. To that purpose we split up the strategy space of each player into a finite number of equivalence classes and consider for a given [epsilon] [greater than] 0 the set of all [epsilon]-proper pairs within the cartesian product of two equivalence classes. If this set is non-empty, its closure is a polytope. By considering this polytope as [epsilon] goes to zero, we obtain a (Myerson) set of proper equilibria. A Myerson set appears to be a polytope.

Date: 1993
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