Robust Distributed Nash Equilibrium Seeking for Discrete-Time Agents

This paper investigates the distributed Nash equilibrium seeking problem of N players with discrete-time dynamics under jointly strongly connected switching networks. First, by integrating gradient play technique with a novel discrete-time distributed observer design, we develop a discretetime distributed Nash equilibrium seeking controller to solve the problem. Next, we establish two technical lemmas to analyze the uniform exponential stability of discrete-time linear switched systems. Then, we obtain the exponential stability of the interconnected closed-loop systems by constructing a Lyapunov function and providing a controller gain design method with the small gain arguments. Finally, the discrete-time distributed Nash equilibrium seeking is achieved over jointly strongly connected switching communication networks. The effectiveness of the developed approach is demonstrated by a numerical simulation example.