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.

中文翻译：

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有向通信网络上部分决策信息下的纳什均衡寻求

我们在部分决策信息场景中考虑纳什均衡问题。具体而言，每个代理只能通过通信网络从某些邻居接收信息，而其成本函数取决于可能所有代理的策略。特别是，虽然现有方法假设无向或平衡的通信，但在本文中，我们允许非平衡的有向图。我们提出了一个完全分布的伪梯度方案，它保证在游戏映射的强单调性和 Lipschitz 连续性下以线性速率收敛到纳什均衡。我们的算法需要通信结构的全局知识，即邻接矩阵的 Perron-Frobenius 特征向量和与图连通性相关的某个常数。所以，