Distributed Nash Equilibrium Seeking for Constrained Aggregative Games over Jointly Connected and Weight-Balanced Switching Networks

TL;DR

This paper develops a distributed algorithm for finding Nash equilibria in constrained aggregative games over dynamic, directed, and weight-balanced switching networks, ensuring exponential stability.

Contribution

It introduces a novel approach combining projected gradient and dynamic consensus techniques for constrained games over complex switching networks.

Findings

Proves exponential stability of the proposed algorithm.

Handles directed and disconnected switching networks.

Extends Nash equilibrium seeking to constrained, dynamic network settings.

Abstract

The property of the communication network and the constraints on the strategic space are two factors that determine the complexity of the distributed Nash equilibrium (DNE) seeking problem. The DNE seeking problem of aggregative games has been studied for unconstrained case over all types of communication networks and for various types of constrained games over static and connected communication networks. In this paper, we investigate the DNE seeking problem for constrained aggregative games over jointly connected and weight-balanced switching networks, which can be directed and disconnected at every time instant. By integrating the projected gradient technique and the dynamic average consensus algorithm, we convert our problem to the stability problem of a well-defined time-varying nonlinear system. By constructing a time-varying Lyapunov's function candidate for this time-varying nonlinear system, we conduct a rigorous Lyapunov's analysis to conclude the exponential stability of this system and hence solve our problem.