A consensus-based algorithm for non-convex multiplayer games

In this paper, we present a novel consensus-based zeroth-order algorithm tailored for non-convex multiplayer games. The proposed method leverages a metaheuristic approach using concepts from swarm intelligence to reliably identify global Nash equilibria. We utilize a group of interacting particles, each agreeing on a specific consensus point, asymptotically converging to the corresponding optimal strategy. This paradigm permits a passage to the mean-field limit, allowing us to establish convergence guarantees under appropriate assumptions regarding initialization and objective functions. Finally, we conduct a series of numerical experiments to unveil the dependency of the proposed method on its parameters and apply it to solve a nonlinear Cournot oligopoly game involving multiple goods.