Integral global optimization method for nonlinear games

Abstract

A derivative-free method for global solution of continuous nonlinear games is proposed. The method is based on the integral global optimization algorithm for mathematical programming and it does not employ gradient-based techniques nor the notion of convexity. The existence of a saddle point is not assumed a priori. Instead, the method delivers the global solutions for both players, and, if global saddle points exist, it yields the value of the game and the global saddle set. Several computational schemes are proposed and nonlinear games with uncertainties are considered. The ideas are illustrated by examples.