Distributed Nash Equilibrium Seeking Algorithm for Aggregative Games with Time-Varying Directed Communication Networks

A distributed discrete Nash equilibrium (NE) seeking algorithm is designed for aggregative games (AGs) through multi-round communications under the restricted strongly monotone assumption. Every agent can observe its own cost function and strategy, and access information only of neighbors according to the time-varying directed communication networks. Then, the proposed algorithm where the number of communications per iteration is fixed turns out to converge to a unique NE point and the rate of convergence is linear. The complexity of the algorithm in this paper is lower compared with others of increasing communication rounds. Finally, a networked Nash-Cournot game is considered to show the accuracy of the algorithm.