Distributed Nash Equilibrium Seeking under Partial-Decision Information via the Alternating Direction Method of Multipliers

TL;DR

This paper introduces a fast, convergent algorithm based on inexact-ADMM for finding Nash equilibria in multi-player games with partial information and complex communication structures, outperforming traditional methods.

Contribution

It proposes a novel inexact-ADMM-based algorithm for Nash equilibrium seeking under partial information and network heterogeneity, with proven convergence and rate analysis.

Findings

Algorithm converges to Nash equilibrium with fixed step-sizes.

Numerical results show improved performance over consensus-based gradient methods.

Convergence rate analysis confirms efficiency of the proposed method.

Abstract

In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their opponents and the communication graph is not necessarily the same as the players' cost dependency graph. We develop a relatively fast algorithm within the framework of inexact-ADMM, based on local information exchange between the players. We prove its convergence to Nash equilibrium for fixed step-sizes and analyze its convergence rate. Numerical simulations illustrate its benefits when compared to a consensus-based gradient type algorithm with diminishing step-sizes.