Distributed Nash Equilibrium Seeking for Second-Order Players With Time-Varying Measurement Delays

This article studies the distributed Nash equilibrium seeking problem for second-order players with time-varying measurement delays, where each player can only obtain the delayed information of its own action and its neighbors' actions without any velocity information. Under a strongly connected communication graph, a novel distributed algorithm consisting of a predictor and a distributed estimator is designed, which effectively compensates for the influence of time-varying measurement delays and enables each player to estimate other players' actions. A new Lyapunov-Krasovskii functional is constructed to perform the convergence analysis of the designed algorithm, and it is proved that the actions of all players globally exponentially converge to the Nash equilibrium. Finally, simulation examples are provided to verify the effectiveness of the proposed methods.