A Multiple Objective Approach to Nash Equilibria in Bimatrix Games

Abstract

Nash equilibria of bimatrix games may be found by solving a nonconvex quadratic multiple objective programming problem over a linear constraint set. The advantages over traditional approaches are explored. Every efficient solution is a Nash equilibrium point, so one may easily obtain multiple equilibria, which is a capability not found in other approaches. Since it is known that Nash equilibria exist, one also obtains a proof that efficient solutions exist for these nonconvex quadratic multiple objective programming problems. Finally, there is an interesting new interpretation of Nash equilibria obtained, namely, that a multiple objective referee of the game exists, who ensures the optimal play by the two participants.KeywordsNash equilibriumbimatrix gamesefficient solutionsmultiple objective quadratic programminglinear complementarity problems