Differentially Private Distributed Nash Equilibrium Seeking over Time-Varying Digraphs

TL;DR

This paper introduces a differentially private distributed algorithm for Nash equilibrium seeking in aggregative games over dynamic directed networks, ensuring convergence and privacy without trade-offs.

Contribution

It presents a novel algorithm combining Laplace noise injection, push-sum consensus, and momentum to achieve privacy-preserving Nash equilibrium seeking over time-varying graphs.

Findings

Ensures almost sure convergence of the algorithm.

Provides rigorous differential privacy guarantees.

Demonstrates effectiveness through simulations.

Abstract

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. Then, the push-sum consensus protocol is utilized to estimate the aggregate function with the perturbed information under the time-varying topologies. The weakening factor and the momentum term are designed to attenuate the negative affect of the noise and guarantee the convergence of the algorithm, respectively. The algorithm is then 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.