New Differential Evolution Selective Mutation Operator for the Nash Equilibria Problem

Differential Evolution (DE) is a simple and powerful optimization method, which is mainly applied to numerical optimization. In this article we present a new selective mutation operator for the Differential Evolution. We adapt the Differential Evolution algorithm to the problem of finding the approximate Nash equilibrium in n person games in the strategic form. Finding the Nash equilibrium 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 the Nash approximation and called is an element of-Nash equilibrium. The fitness function in this approach is based on the max function which selects the maximal value from the set of payoffs. Every element of this set is calculated on the basis of the corresponding genotype part. We propose an approach, which allows us to modify only the worst part of the genotype. Mainly, it allows to decrease computation time and slightly improve the results.