Approximate Nash Equilibria in Bimatrix Games

Nash equilibrium is one of the main concepts in the game theory. Recently it was shown, that problem of finding Nash equilibrium and an approximate Nash equilibrium is PPAD-complete. In this article we adapt Differential Evolution algorithm (DE) to the above problem. It may be classified as continuous problem, where two probability distributions over the set of pure strategies of both players should be found. Every deviation from the global optimum is interpreted as Nash approximation and called epsilon-Nash equilibrium. We show, that the Differential Evolution approach can be determined as iterative method, which in successive iterations is capable to obtain epsilon value close to the global optimum. The contribution of this paper is the experimental analysis of the proposed approach and indication of it's strong features. We try to demonstrate, that the proposed method is very good alternative for the existing mathematical analysis of the mentioned Nash equilibrium problem.