The distributed computation of a Nash equilibrium in aggregative games is gaining increased traction in recent years. Of particular interest is the mediator-free scenario where individual players only access or observe the decisions of their neighbors due to practical constraints. Given the competitive rivalry among participating players, protecting the privacy of individual players becomes imperative when sensitive information is involved. We propose a fully distributed equilibrium-computation approach for aggregative games that can achieve both rigorous differential privacy and guaranteed computation accuracy of the Nash equilibrium. This is in sharp contrast to existing differential-privacy solutions for aggregative games that have to either sacrifice the accuracy of equilibrium computation to gain rigorous privacy guarantees, or allow the cumulative privacy budget to grow unbounded, hence losing privacy guarantees, as iteration proceeds. Our approach uses independent noises across players, thus making it effective even when adversaries have access to all shared messages as well as the underlying algorithm structure. The encryption-free nature of the proposed approach, also ensures efficiency in computation and communication. The approach is also applicable in stochastic aggregative games, able to ensure both rigorous differential privacy and guaranteed computation accuracy of the Nash equilibrium when individual players only have stochastic estimates of their pseudo-gradient mappings. Numerical comparisons with existing counterparts confirm the effectiveness of the proposed approach.

翻译：近年来，聚合博弈中纳什均衡的分布式计算日益受到关注。特别值得关注的是无中介场景，其中由于实际约束，个体参与者仅能获取或观察其邻居的决策。鉴于参与者之间的竞争关系，当涉及敏感信息时，保护个体参与者的隐私变得至关重要。我们提出了一种完全分布式聚合博弈均衡计算方法，该方法能够同时实现严格的差分隐私和纳什均衡计算精度的保证。这与现有的聚合博弈差分隐私解决方案形成鲜明对比，后者要么需要牺牲均衡计算精度以获得严格的隐私保证，要么允许累积隐私预算随着迭代进行而无限增长，从而丧失隐私保证。我们的方法在参与者之间使用独立噪声，因此即使在对手能够获取所有共享消息以及底层算法结构的情况下，依然有效。所提方法无需加密，从而保证了计算与通信的高效性。该方法同样适用于随机聚合博弈，当个体参与者仅能获得其伪梯度映射的随机估计时，仍能同时确保严格的差分隐私和纳什均衡的计算精度。与现有方法的数值对比验证了所提方法的有效性。