Comparative study of the differential evolution and approximation algorithms for computing optimal mixed strategies in zero-sum games

Abstract

In this paper, we present the application of the Differential Evolution (DE) algorithm to the problem of finding optimal mixed strategies in zero-sum games for two players. Differential evolution (DE) is a simple and powerful optimization method, which is mainly applied to numerical optimization and many other problems (for example: neural network train, filter design or image analysis). The advantage of the DE algorithm is its capability of avoiding so-called "local minima" within the considered search space. Thanks to the special operator of the adaptive mutation, it is possible to direct the searching process within the solution space. Approach used in this article is based on the probability of selecting single pure strategy. In optimal mixed strategy, every strategy has some probability of being chosen. Our goal is determine this probability and maximize payoff for a single player. We also compare proposed method with well known approximation algorithm. © 2010 Springer-Verlag Berlin Heidelberg.