Distributed Fixed-time Nash Equilibrium Seeking for Noncooperative Games

This paper investigates the fixed-time Nash equilibrium seeking for noncooperative games over networked players, where the players are supposed to have only access to the actions of their neighboring players. Novel consensus-based distributed fixed-time Nash equilibrium seeking strategies are proposed for players with both the first- and second-order dynamics. Via Lyapunov-based techniques, it is proved that under the proposed strategies, the actions of players with both first- and second-order dynamics can converge to the Nash equilibrium within a fixed time, which is upper bounded by a finite constant independent of the players' initial conditions. Simulation results are provided to verify the effectiveness of the proposed seeking strategies.