Generalized Nash equilibrium seeking for directed nonsmooth multi-cluster games via a distributed Lipschitz algorithm

This paper investigates a generalized Nash equilibrium (GNE) seeking strategy for a class of nonsmooth multi-cluster games. Each cluster consists of several players. The inter-cluster graph is directed and weight-unbalanced. Moreover, in contrast to previous works of multi-cluster games, coupled nonsmooth inequality constraints, resource allocation constraints, and nonsmooth payoff functions are considered simultaneously in these multi-cluster games. For seeking the GNE of these games, a distributed Lipschitz algorithm with the proximal-splitting scheme is proposed. Then convergence analysis of this designed algorithm is deduced based on Lyapunov stability theory and convex optimization theory. Finally, some simulation results are provided in this paper, which show the efficacy of the distributed GNE seeking algorithm.