Adaptive approaches for fully distributed Nash equilibrium seeking in networked games
Abstract: 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.
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