Distributed Nash Equilibrium Seeking of Noncooperative Games with Communication Constraints and Matrix Weights

Distributed Nash equilibrium seeking is investigated in this paper for a class of multi-agent systems under intermittent communication and matrix-weighted communication graphs. Different from most of the existing works on distributed Nash equilibrium seeking of noncooperative games where the players (agents) can communicate continuously over time, the players considered in this paper are assumed to exchange information only with their neighbors during some disconnected time intervals while the underlying communication graph is matrix-weighted. A distributed Nash equilibrium seeking algorithm integrating gradient strategy and leader-following consensus protocol is proposed for the noncooperative games with intermittent communication and matrix-weighted communication graphs. The effect of the average intermittent communication rate on the convergence of the distributed Nash equilibrium seeking algorithm is analyzed, and a lower bound of the average intermittent communication rate that ensures the convergence of the algorithm is given. The convergence of the algorithm is established by means of Lyapunov stability theory. Simulations are presented to verify the proposed distributed Nash equilibrium seeking algorithm.