Fast Distributed Nash Equilibrium Seeking in Monotone Games

TL;DR

This paper introduces a fast, distributed algorithm for finding Nash equilibria in convex monotone games, leveraging operator extrapolation techniques to achieve geometric convergence with limited communication.

Contribution

It develops a novel distributed method based on operator extrapolation for Nash equilibrium seeking in monotone games, improving convergence rates over previous approaches.

Findings

Converges geometrically to Nash equilibria.

Operates with limited communication among players.

Outperforms previous algorithms in convergence speed.

Abstract

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [5] to solve variational inequalities, we develop the algorithm converging to Nash equilibria in games, where players have no access to the full information but are able to communicate with neighbors over some communication graph. The convergence rate is demonstrated to be geometric and improves the rates obtained by the previously presented procedures seeking Nash equilibria in the class of games under consideration.