Statistical Privacy-Preserving Online Distributed Nash Equilibrium Tracking in Aggregative Games

Abstract

This article considers an online aggregative game equilibrium problem subject to privacy preservation, where all players aim at tracking the time-varying Nash equilibrium, while some players are corrupted by an adversary. We propose a distributed online Nash equilibrium tracking algorithm, where a correlated perturbation mechanism is employed to mask the local information of the players. Our theoretical analysis shows that the proposed algorithm can achieve a sublinear expected regret bound while preserving the privacy of uncorrupted players. We use the Kullback–Leibler divergence to analyze the privacy bound in a statistical sense. Furthermore, we present a tradeoff between the expected regret and the statistical privacy, to obtain a constant privacy bound when the regret bound is sublinear.