Online Nash Equilibrium Seeking with Time-Varying Payoff Functions

In this paper, we consider the continuous-time Nash equilibrium seeking problem with time-varying payoff functions. To solve the problem, we first propose an extended version of distributed gradient play algorithms using exact real-time gradients. Then, we discuss its performance from the perspective of online computation, and show that the proposed algorithm can lead to some small dynamic regret providing that the real-time Nash equilibrium does not change too fast. We finally provide a numerical example to illustrate our design.