Distributed Nash Equilibrium Seeking in Aggregative Games over Jointly Connected and Weight-Balanced Networks

Abstract: The problem of the distributed Nash equilibrium seeking for aggregative games has been studied over strongly connected and weight-balanced static networks and every time strongly connected and weight-balanced switching networks. In this paper, we further study the same problem over jointly connected and weight-balanced networks. The existing approaches critically rely on the connectedness of the network for constructing a Lyapunov function for their algorithms and theses approaches fail if the network is not connected. To overcome this difficulty, we propose an approach to show the exponential convergence of the output of the closed-loop system to the unknown Nash equilibrium (NE) point under a set of mild conditions.