Continuous-time integral dynamics for Aggregative Game equilibrium seeking

TL;DR

This paper introduces a continuous-time semi-decentralized integral control scheme for aggregative games, proving global exponential convergence to equilibrium with improved conditions over existing methods.

Contribution

It proposes a novel integral control-based dynamics for aggregative games and establishes improved convergence conditions compared to prior work.

Findings

Global exponential convergence is proven under new sufficient conditions.

The proposed scheme outperforms existing methods in convergence guarantees.

A quadratic Lyapunov function is used to analyze stability.

Abstract

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.