论文标题
关于分布式NASH平衡的线性收敛，寻求在部分决策信息下为多群集游戏
On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information
论文作者
论文摘要
本文考虑了在部分决策信息方案下在多群集游戏中寻求NASH平衡（NE）的分布式策略设计。在考虑的游戏中，有多个集群，每个集群由一组代理组成。群集被视为一个虚拟的非合作播放器，旨在最大程度地减少其本地收益功能，而集群中的代理是在集群中合作的实际玩家，可以通过连接的图形通过通信来优化群集的回报功能。在我们的环境中，代理只有部分决策信息，也就是说，他们只知道本地信息，并且无法完全访问对手的决定。为了解决该公式游戏的NE寻求问题，根据集群的间和内部交流，设计了一种称为分布式梯度跟踪算法（DGT）的离散时间分布式算法，称为分布式梯度跟踪算法（DGT）。在设计算法中，每个代理都配备了策略变量，包括其自身的策略和其他簇策略的估计。借助加权的fronbenius标准和加权欧几里得规范，理论分析被提出以严格显示算法的线性收敛性。最后，给出了一个数值示例来说明所提出的算法。
This paper considers the distributed strategy design for Nash equilibrium (NE) seeking in multi-cluster games under a partial-decision information scenario. In the considered game, there are multiple clusters and each cluster consists of a group of agents. A cluster is viewed as a virtual noncooperative player that aims to minimize its local payoff function and the agents in a cluster are the actual players that cooperate within the cluster to optimize the payoff function of the cluster through communication via a connected graph. In our setting, agents have only partial-decision information, that is, they only know local information and cannot have full access to opponents' decisions. To solve the NE seeking problem of this formulated game, a discrete-time distributed algorithm, called distributed gradient tracking algorithm (DGT), is devised based on the inter- and intra-communication of clusters. In the designed algorithm, each agent is equipped with strategy variables including its own strategy and estimates of other clusters' strategies. With the help of a weighted Fronbenius norm and a weighted Euclidean norm, theoretical analysis is presented to rigorously show the linear convergence of the algorithm. Finally, a numerical example is given to illustrate the proposed algorithm.
