We propose fully-distributed algorithms for Nash equilibrium seeking in aggregative games over networks. We first consider the case where local constraints are present and we design an algorithm combining, for each agent, (i) the projected pseudo-gradient descent and (ii) a tracking mechanism to locally reconstruct the aggregative variable. To handle coupling constraints arising in generalized settings, we propose another distributed algorithm based on (i) a recently emerged augmented primal-dual scheme and (ii) two tracking mechanisms to reconstruct, for each agent, both the aggregative variable and the coupling constraint satisfaction. Leveraging tools from singular perturbations analysis, we prove linear convergence to the Nash equilibrium for both schemes. Finally, we run extensive numerical simulations to confirm the effectiveness of our methods and compare them with state-of-the-art distributed equilibrium-seeking algorithms.

翻译：我们提出完全分布式算法用于网络化聚合博弈中的纳什均衡求解。首先考虑存在局部约束的情形，为每个智能体设计了一种结合(1)投影伪梯度下降法与(2)追踪机制的算法，以实现聚合变量的局部重构。针对广义场景中出现的耦合约束，提出另一种基于(1)近期发展的增广原始-对偶框架及(2)双重追踪机制（用于为每个智能体重构聚合变量与耦合约束满足度）的分布式算法。借助奇异摄动分析工具，证明了两种方案的纳什均衡线性收敛性。最终通过大量数值仿真验证了方法的有效性，并与现有最先进的分布式均衡寻求算法进行了对比。