We address differential privacy for fully distributed aggregative games with shared coupling constraints. By co-designing the generalized Nash equilibrium (GNE) seeking mechanism and the differential-privacy noise injection mechanism, we propose the first GNE seeking algorithm that can ensure both provable convergence to the GNE and rigorous epsilon-differential privacy, even with the number of iterations tending to infinity. As a basis of the co-design, we also propose a new consensus-tracking algorithm that can achieve rigorous epsilon-differential privacy while maintaining accurate tracking performance, which, to our knowledge, has not been achieved before. To facilitate the convergence analysis, we also establish a general convergence result for stochastically-perturbed nonstationary fixed-point iteration processes, which lie at the core of numerous optimization and variational problems. Numerical simulation results confirm the effectiveness of the proposed approach.

翻译：我们研究了具有共享耦合约束的完全分布式聚合博弈中的差分隐私问题。通过协同设计广义纳什均衡（GNE）求解机制与差分隐私噪声注入机制，我们首次提出了一种GNE求解算法，该算法即使在迭代次数趋于无穷的情况下，也能同时保证可证明的GNE收敛性和严格的ε-差分隐私。作为协同设计的基础，我们还提出了一种新的共识跟踪算法，该算法能够在保持精确跟踪性能的同时实现严格的ε-差分隐私，据我们所知，这在之前尚未实现。为便于收敛性分析，我们还建立了一个针对随机扰动非平稳不动点迭代过程的一般性收敛结果，该过程是众多优化和变分问题的核心。数值仿真结果验证了所提方法的有效性。