On weakly completely mixed bimatrix games

Abstract

Weakly completely mixed bimatrix games are defined to be games with a completely mixed Nash component. For these games this component turns out to consist of only one point, which is isolated. Special classes of these games are completely mixed matrix and bimatrix games, the first introduced by Kaplansky, the latter by Raghavan. We give a characterization of these games, which can be used for completely mixed matrix games also. Given a completely mixed strategy pair, we are able to construct a (weakly) completely mixed bimatrix game having this pair as an equilibrium. We derive interesting results for the case where the payoff matrices have a nonnegative and irreducible inverse.