Global Nash Equilibrium in a Class of Nonconvex N-player Games

Guanpu Chen, Gehui Xu, Yiguang Hong

Abstract: We consider seeking the global Nash equilibrium (NE) in a class of nonconvex N-player games. The structured nonconvex payoffs are composited with canonical functions and quadratic operators, which are broadly investigated in various tasks such as robust network training and sensor network communication. However, the full-fledged development of nonconvex min-max games may not provide available help due to the interference of multiple players’ coupled stationary conditions, and the existing results on convex games may also perform unsatisfactorily since they may be stuck in local NE or Nash stationary points, rather than the global NE. Here, we first make efforts to take a canonical conjugate transformation of the nonconvex N-player game, and cast the complementary problem into a variational inequality (VI) problem for the derivation of the global NE. Then we design a conjugate-based ordinary differential equation (ODE) for the solvable VI problem, and present the equilibrium equivalence and guaranteed convergence within the ODE. Furthermore, we provide a discretized algorithm based on the ODE, and discuss step-size settings and convergence rates in two typical nonconvex N-player games. At last, we conduct experiments in practical tasks to illustrate the effectiveness of our approach.

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