论文标题
基于跟踪的分布均衡寻求聚合游戏
Tracking-based distributed equilibrium seeking for aggregative games
论文作者
论文摘要
我们建议在网络上的总体游戏中寻求NASH平衡的完全分布算法。我们首先考虑存在局部约束并为每个代理设计算法组合的情况。为了处理在广义设置中产生的耦合约束，我们根据（i）最近出现的增强原始偶对偶偶联方案提出了另一种分布式算法，以及（ii）为每个代理重建的两个跟踪机制，即聚集变量和耦合约束满意度。利用奇异扰动分析的工具，我们证明了这两个方案的NASH平衡线性收敛。最后，我们运行了广泛的数值模拟，以确认方法的有效性，并将其与最先进的分布式平衡算法进行比较。
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.
