Differentially private distributed nash equilibrium seeking based on gradient tracking and communication compression

Communication efficiency and privacy preservation are two critical challenges in distributed Nash equilibrium (NE) seeking for multi-agent systems. In this paper, we propose a novel algorithm, CGT-DPA, which integrates gradient tracking to enhance information aggregation and ensure convergence, while incorporating communication compression to significantly reduce communication overhead. Additionally, the algorithm enforces differential privacy, providing strong privacy guarantees in distributed settings. We rigorously prove that CGT-DPA achieves linear convergence to a neighborhood of the NE under strongly monotone mappings. Both theoretical analysis and numerical simulations validate the effectiveness of CGT-DPA in balancing communication efficiency, privacy preservation and convergence.