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

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.