Computing Generalized Nash Equilibria by Polynomial Programming

We present a new way to solve generalized Nash equilibrium problems. We assume the feasible set to be compact. Furthermore all functions are assumed to be polynomials. However we do not need any convexity assumptions on either the utility functions or the action sets. The key idea is to use Putinar's Positivstellensatz, a representation result for positive polynomials, to replace each agent's problem by a convex optimization problem. The Nash equilibria are then feasible solutions to a system of polynomial equations and inequalities. Our application is a model of the New Zealand electricity spot market with transmission losses based on a real dataset