Deng Zhenhua, Liu Yangyang
IEEE Trans Neural Netw Learn Syst. 2023 Dec;34(12):10802-10811. doi: 10.1109/TNNLS.2022.3171535. Epub 2023 Nov 30.
In this article, we study the multicluster games over weight-balanced digraphs, where the cost functions of all players are nonsmooth. Besides, in the problem, not only are the decisions of all players constrained by heterogeneous local constraints but also the decisions of players in the same cluster are constrained by coupling constraints. Due to the nonsmooth cost functions, the coupling constraints, the general local convex constraints, and the weight-balanced digraphs, existing Nash equilibrium seeking algorithms cannot solve our problem. In order to seek the Nash equilibrium of the game, we design a distributed algorithm based on subgradient descent, differential inclusions, and projection operations. In the algorithm, a distributed learning strategy is embedded for the players to estimate the decisions of other players. Moreover, we analyze the asymptotical convergence of the algorithm via set-valued LaSalle invariance principle. Finally, a numerical simulation about electricity market games is presented to illustrate the effectiveness of our result.
在本文中，我们研究了加权平衡有向图上的多簇博弈，其中所有参与者的成本函数都是非光滑的。此外，在该问题中，不仅所有参与者的决策受到异构局部约束的限制，而且同一簇中参与者的决策还受到耦合约束的限制。由于成本函数非光滑、耦合约束、一般局部凸约束以及加权平衡有向图的存在，现有的纳什均衡寻求算法无法解决我们的问题。为了寻求博弈的纳什均衡，我们设计了一种基于次梯度下降、微分包含和投影运算的分布式算法。在该算法中，为参与者嵌入了一种分布式学习策略，以估计其他参与者的决策。此外，我们通过集值拉萨尔不变性原理分析了算法的渐近收敛性。最后，给出了一个关于电力市场博弈的数值模拟，以说明我们结果的有效性。
