Nash equilibria in normal games via optimization methods

This paper is devoted to Nash equilibria of normal-form games. We give a survey on computing Nash equilibria via optimization methods. Further on we prove, that the Nash equilibria of a game coincide with the zeros of a nonlinear, almost everywhere smooth system of equations with the same dimension as the strategy space. Thus, we can apply tools for solving nonlinear systems of equations. We present an algorithm for computing Nash equilibria, which has shown very satisfactory results.