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.

翻译：本文研究全分布式纳什均衡求解中的隐私保护问题，其中每个参与方仅能访问自身代价函数，并通过有向通信网络接收其近邻信息。鉴于底层决策过程的非合作性质，当涉及敏感信息时，保护网络博弈中个体参与方的隐私至关重要。我们提出了一种方法，可在分布式纳什均衡求解中同时实现精确收敛与有限累积隐私预算下的严格差分隐私，这与现有需以收敛精度换取差分隐私的网络博弈算法形成鲜明对比。该方法甚至适用于非平衡通信图，且无需个体参与方掌握通信图的任何全局结构信息。由于采用独立噪声进行隐私保护，该方法能抵御可访问网络中所有共享消息的对手攻击，同时无需加密，确保了通信与计算的高效性。与现有方法的数值对比结果验证了所提方法的有效性。