A novel approximate method of computing extended Nash equilibria

Abstract

In this paper, we propose a new method of computing an approximate Nash equilibrium with additional features. Existing algorithms often fail to produce an exact solution for games involving more than 3 players. Similarly, existing algorithms do not permit additional constraints on the problem. The principle idea of this paper involves proposing a methodology for computing approximate solutions through evolutionary computation. To do so, we first provide formal definitions of these problems and their approximate versions. Following which, we present the details of our solution. One of the most important advantages of the proposed solution is flexibility, which provides solutions to problems related to Nash equilibrium extensions. The proposed idea is tested on several types of games that vary with difficulty and size. All test sets are generated based on the well-known Gamut program. Additional comparisons with classical algorithms are also performed. Results indicate that Differential Evolution is capable of obtaining satisfactory solutions to large random and covariant games. The results also demonstrate that there is a high probability that even large games, in which a set of strategies with a non-zero probability of being chosen are very small, have a solution. The computation time depends mainly on the problem size, and the original Nash equilibrium problem is unaffected by additional modifications.