Distributed Nash Equilibrium Seeking Dynamics With Discrete Communication

In this brief, we aim to provide a distributed Nash equilibrium seeking algorithm in continuous time with discrete communications. A group of agents are considered playing a continuous-kernel noncooperative game over a network. The agents need to seek the Nash equilibrium when each player cannot get the overall action profiles in real time, rather are only able to get information from its networked neighbors. Meanwhile, a continuous-time dynamics is discussed for the players to update their variables, but the communications over the network are only assumed to allow at discrete-time instants, since continuous-time communications are prohibitive and cumbersome in practice. First, the periodic communication is considered at a fixed interval, and the solvability of Nash equilibrium seeking is shown with discrete communications. Then, an event-trigger communication scheme is proposed to further reduce the communication rounds. Nevertheless, the event-trigger communication scheme requires each player continuously monitoring its local states. To alleviate the monitoring burden, a periodic event detection mechanism is further developed. The exponential convergence of the dynamics with the three discrete communication schemes is proven. Finally, the comparative simulation studies are designed to illustrate the algorithm performance with different communication schemes and parameter settings.