This paper concerns the generalized Nash equilibrium problem of polynomials (GNEPP). We apply the Gauss–Seidel method and 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.

中文翻译：

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多项式广义Nash平衡问题的Gauss-Seidel方法

本文涉及多项式的广义纳什均衡问题（GNEPP）。我们应用高斯-塞德尔方法和矩-SOS松弛来解决GNEPPs。高斯-塞德尔方法的收敛性在某些特殊的GNEPP中是众所周知的，例如广义潜在博弈（GPG）。我们为GPG提供了充分的条件，并根据Putinar的Positivstellensatz提出了数字证书。给出了凸和非凸GNEPP的数值示例，以证明所提出方法的效率。