Differentially-private distributed Nash equilibrium seeking via a probabilistic mapping mechanism

This article addresses a non-cooperative game problem subject to privacy leakage, in which the players exchange their messages under limited transmission bandwidth. Based on the vector quantizer adopted to improve the communication efficiency, we propose a novel differentially-private distributed Nash equilibrium seeking algorithm, where a probabilistic mapping mechanism employing truncated discrete noise is designed to mask the quantization levels of exchanged messages. The theoretical analysis demonstrates that our algorithm achieves both exact and linear convergence in the mean-square sense, and also guarantees (ϵ,δ)-differential privacy for the players at each iteration. Additionally, we analyze the impact of privacy parameters on the truncated bound of the discrete noise, and further present a trade-off between the privacy level and convergence rate of our algorithm.