论文标题
NASH平衡在部分决策信息下寻求通过定向通信网络
Nash equilibrium seeking under partial-decision information over directed communication networks
论文作者
论文摘要
我们考虑了部分决策信息方案中的NASH均衡问题。具体来说，每个代理只能通过通信网络从某些邻居那里接收信息，而其成本函数取决于所有代理的策略。特别是，尽管现有方法假设了无方向性或平衡的通信，但在本文中，我们允许使用不均衡的有向图。我们提出了一个完全分布的伪级方案，该方案在强大的单调性和Lipschitz的连续性下，可以保证以线性速率融合到NASH平衡。我们的算法需要对通信结构的全局知识，即邻接矩阵的perron-frobenius特征向量以及与图形连接性相关的一定常数。因此，我们通过在线计算特征向量并通过消失的步骤大小来调整该过程的设置，以设置网络未提前知道。
We consider the Nash equilibrium problem in a partial-decision information scenario. Specifically, each agent can only receive information from some neighbors via a communication network, while its cost function depends on the strategies of possibly all agents. In particular, while the existing methods assume undirected or balanced communication, in this paper we allow for non-balanced, directed graphs. We propose a fully-distributed pseudo-gradient scheme, which is guaranteed to converge with linear rate to a Nash equilibrium, under strong monotonicity and Lipschitz continuity of the game mapping. Our algorithm requires global knowledge of the communication structure, namely of the Perron-Frobenius eigenvector of the adjacency matrix and of a certain constant related to the graph connectivity. Therefore, we adapt the procedure to setups where the network is not known in advance, by computing the eigenvector online and by means of vanishing step sizes.
