Computation of Mixed Strategy Non-dominated Nash Equilibria in Game Theory

Abstract

Finding Nash equilibria has been one of the early objectives of research in game theory, and still represents a challenge to this day. We introduce a multiobjective formulation for computing Pareto-optimal sets of mixed Nash equilibria in normal form games. Computing these sets can be notably useful in decision making, because it focuses the analysis on solutions with greater outcome and hence more stable and desirable ones. While the formulation is suitable for any multiobjective optimization algorithm, we employ a method known as the cone-epsilon MOEA, due to its good convergence and diversity characteristics when solving multiobjective optimization problems. The adequacy of the proposed formulation is tested on most normal form games provided by the GAMBIT software test suite. The results show that the cone-epsilon MOEA working on the proposed formulation correctly finds the Pareto-optimal Nash equilibra in most games.