Distributed Nash Equilibrium Seeking for Multicluster Game Under Switching Communication Topologies

Abstract

In this article, we investigate the distributed Nash equilibrium (NE) seeking problem for the multi-cluster game under switching communication topologies. Specifically, the communication topology switches between a group of jointly connected digraphs. First, a new distributed NE seeking algorithm for the multi-cluster games is designed by the consensus protocol and gradient play rule under the switching communication topologies. Furthermore, in order to make the algorithm still applicable when the agent only knows part of the decision information, the leader-following consensus protocol is used to generate the estimates for all agents action in the cluster under the assumption that the switching topology between clusters is directed and strongly connected. A more general NE seeking algorithm for the multi-cluster games is designed. For these two algorithms, the results of local convergence and non-local convergence are given, respectively. Two examples verify the validity of the theoretical results.