  This paper concerns the generalized Nash equilibrium problem of polynomials
(GNEPP). We apply the Gauss-Seidel method and Lasserre type Moment-SOS
relaxations to solve GNEPPs. The convergence of the Gauss-Seidel method is
known for some special GNEPPs, such as generalized potential games (GPGs). We
give a sufficient condition for GPGs and propose a numerical certificate, based
on Putinar's Positivstellensatz. Numerical examples for both convex and
nonconvex GNEPPs are given for demonstrating the efficiency of the proposed
method.
