Ensuring both Accurate Convergence and Differential Privacy in Nash Equilibrium Seeking on Directed Graphs

We study in this paper privacy protection in fully distributed Nash equilibrium seeking where a player can only access its own cost function and receive information from its immediate neighbors over a directed communication network. In view of the non-cooperative nature of the underlying decision-making process, it is imperative to protect the privacy of individual players in networked games when sensitive information is involved. We propose an approach that can achieve both accurate convergence and rigorous differential privacy with finite cumulative privacy budget in distributed Nash equilibrium seeking, which is in sharp contrast to existing differential-privacy solutions for networked games that have to trade convergence accuracy for differential privacy. The approach is applicable even when the communication graph is unbalanced and it does not require individual players to have any global structure information of the communication graph. Since the approach utilizes independent noises for privacy protection, it can combat adversaries having access to all shared messages in the network. It is also encryption-free, ensuring high efficiency in communication and computation. Numerical comparison results with existing counterparts confirm the effectiveness of the proposed approach.