On the set of proper equilibria of a bimatrix game

This paper proves that the set of proper equilibria of a bimatrix game is the finite union of polytopes. To that purpose it splits up the strategy space of each player into a finite number of equivalence classes and considers for a given •>0 the set of all •-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 • goes to zero, the paper obtains a (Myerson) set of proper equilibria. A Myerson set appears to be a polytope.