This paper considers the design of fully distributed Nash equilibrium seeking strategies for networked games. To develop fully distributed seeking strategies, two adaptive control laws, including a node-based control law and an edge-based control law, are proposed. In the node-based adaptive strategy, each player adjusts their own weight on their procurable consensus error dynamically. Moreover, in the edge-based algorithm, the fully distributed strategy is designed by adding an adaptively adjusted scaling parameter to the weights of the edges of the communication graph. With the adaptive control laws, the proposed methods are free of any centralized control gains, i.e., the players can update their actions without knowing any centralized information. By utilizing LaSalle’s invariance principle, it is shown that the Nash equilibrium is globally asymptotically stable under both strategies. In addition, we further show that the edge-based method can be easily adapted to accommodate time-varying communication conditions, in which the communication network is switching among a set of undirected and connected graphs. In the last, numerical examples are given to illustrate the effectiveness of the proposed methods.

本文考虑了网络游戏的全分布式纳什均衡寻求策略的设计。为了发展完全分布式的寻找策略，提出了两种自适应控制律，包括基于节点的控制律和基于边缘的控制律。在基于节点的自适应策略中，每个参与者都针对可获取的共识误差动态调整自己的权重。此外，在基于边缘的算法中，通过向通信图的边缘权重添加自适应调整的缩放参数来设计完全分布式策略。利用自适应控制定律，所提出的方法没有任何集中控制增益，即，玩家可以在不知道任何集中信息的情况下更新其动作。利用LaSalle的不变性原理表明，在两种策略下，纳什均衡都是全局渐近稳定的。此外，我们进一步表明，基于边缘的方法可以轻松地适应时变通信条件，其中通信网络在一组无向图和连接图之间进行切换。最后，通过算例说明了所提方法的有效性。