Distributed Nash Equilibrium Seeking via the Alternating Direction Method of Multipliers

TL;DR

This paper introduces a fast distributed algorithm based on inexact-ADMM for multi-player games to find Nash equilibria, requiring minimal assumptions and demonstrating convergence and efficiency through simulations.

Contribution

It develops a novel inexact-ADMM based method for distributed Nash equilibrium seeking with convergence guarantees.

Findings

Algorithm converges to Nash equilibrium

Achieves faster convergence compared to existing methods

Effective in networks with communication constraints

Abstract

In this paper, the problem of finding a Nash equilibrium of a multi-player game is considered. The players are only aware of their own cost functions as well as the action space of all players. We develop a relatively fast algorithm within the framework of inexact-ADMM. It requires a communication graph for the information exchange between the players as well as a few mild assumptions on cost functions. The convergence proof of the algorithm to a Nash equilibrium of the game is then provided. Moreover, the convergence rate is investigated via simulations.