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

TL;DR

This paper develops a distributed method for finding Nash equilibria in aggregative games over jointly connected, weight-balanced networks, ensuring exponential convergence without requiring the network to be constantly connected.

Contribution

It introduces a novel approach that guarantees exponential convergence of the algorithm over jointly connected networks, relaxing the need for persistent network connectivity.

Findings

Proposes a new distributed Nash equilibrium seeking algorithm.

Proves exponential convergence under mild conditions.

Works over jointly connected, 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.