Robust Additively Coupled Games

TL;DR

This paper introduces a framework for analyzing robust Nash equilibria in communication networks under uncertainty, providing existence, uniqueness, and distributed algorithms, with validation through simulations in power control and network scenarios.

Contribution

It develops conditions for the existence and uniqueness of robust Nash equilibria in additive games with uncertainties, and proposes a distributed algorithm for reaching RNE.

Findings

Existence and uniqueness conditions for RNE are derived.

A distributed algorithm for RNE convergence is proposed.

Simulations validate the theoretical analysis in power control and network models.

Abstract

We study the robust Nash equilibrium (RNE) for a class of games in communications systems and networks where the impact of users on each other is an additive function of their strategies. Each user measures this impact, which may be corrupted by uncertainty in feedback delays, estimation errors, movements of users, etc. To study the outcome of the game in which such uncertainties are encountered, we utilize the worst-case robust optimization theory. The existence and uniqueness conditions of RNE are derived using finite-dimensions variational inequalities. To describe the effect of uncertainty on the performance of the system, we use two criteria measured at the RNE and at the equilibrium of the game without uncertainty. The first is the difference between the respective social utility of users and, the second is the differences between the strategies of users at their respective equilibria. These differences are obtained for the case of a unique NE and multiple NEs. To reach the RNE, we propose a distributed algorithm based on the proximal response map and derive the conditions for its convergence. Simulations of the power control game in interference channels, and Jackson networks validate our analysis.