Exponentially convergent distributed Nash equilibrium seeking for constrained aggregative games

TL;DR

This paper introduces a continuous-time distributed algorithm for finding Nash equilibria in constrained aggregative games, ensuring exponential convergence under certain communication conditions, with demonstrated effectiveness through numerical examples.

Contribution

The paper proposes a novel continuous-time distributed algorithm combining projected gradient and average tracking dynamics for constrained aggregative games, achieving exponential convergence.

Findings

Algorithm converges exponentially to Nash equilibrium.

Effective in games with constrained strategies and weight-balanced graphs.

Numerical examples confirm practical effectiveness.

Abstract

Distributed Nash equilibrium seeking of aggregative games is investigated and a continuous-time algorithm is proposed. The algorithm is designed by virtue of projected gradient play dynamics and distributed average tracking dynamics, and is applicable to games with constrained strategy sets and weight-balanced communication graphs. We obtain an exponential convergence of the proposed algorithm to the Nash equilibrium. Numerical examples illustrate the effectiveness of our methods.