Differentially Private Distributed Nash Equilibrium Seeking Over Time-Varying Digraphs

This paper proposes a new differentially private distributed Nash equilibrium seeking algorithm for aggregative games under time-varying unbalanced directed communication graphs. Random independent Laplace noises are injected into the transmitted information to protect players' sensitive information. The push-sum consensus protocol is utilized to estimate the aggregate function with the perturbed information under the time-varying topologies. The momentum term and the noise value of the future moment are designed to guarantee the acceleration and convergence of the algorithm. The proposed algorithm is proven to ensure the almost sure convergence, as well as rigorous differential privacy with a finite cumulative privacy budget, without requiring a trade-off between provable convergence and differential privacy. Finally, the simulation is provided to demonstrate the effectiveness of the proposed algorithm.