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。由于实际约束，个体参与者仅能获取或观察其邻居决策的无需中介场景尤为引人关注。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。本文提出了一种完全分布式的聚合博弈均衡计算方法，该方法既能实现严格的差分隐私，又能保证纳什均衡的计算精度。这与现有聚合博弈差分隐私方案形成鲜明对比——现有方案要么牺牲均衡计算精度以换取严格的隐私保证，要么允许累积隐私预算无限增长，从而随着迭代进行丧失隐私保证。我们的方法在参与者之间使用独立噪声，因此即使攻击者能够访问所有共享消息及底层算法结构，该方案依然有效。所提方法无需加密，确保了计算与通信效率。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与纳什均衡的计算精度。与现有方案的数值对比验证了所提方法的有效性。