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 ɛ >0 the set of all ɛ-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 ɛ goes to zero, we obtain a (Myerson) set of proper equilibria. A Myerson set appears to be a polytope.
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