An optimization method for Nash equilibrium problems

Abstract

The Nash equilibrium problem has attracted much attention in recent years but the standard optimization method cannot be directly used for the problem since it involves several optimization problems that are linked together by the well-known Nash equilibrium concept. Using a regularized Nikaido-Isoda-function, we present a standard optimization problem, which is a complete reformulation of the Nash equilibrium problem in the sense that the global minima of this standard optimization problem are precisely the solutions of the Nash equilibrium problem.