A Linearly Convergent Distributed Nash Equilibrium Seeking Algorithm for Aggregative Games Over Time-Varying Unbalanced Graphs

This article investigates an aggregative game with local closed convex set constraints over time-varying unbalanced communication graphs, and aims to compute the Nash equilibrium (NE) in a distributed manner. To this end, we propose a distributed discrete-time NE seeking algorithm. It combines the average tracking technique and the push-sum protocol to estimate the global aggregate over time-varying unbalanced graphs, and incorporates the method of feasible direction to handle the set constraints. Based on the small gain theorem, we establish the linear convergence of the proposed algorithm and provide explicit estimates for the step-size upper bounds. Finally, numerical simulations of a Nash-Cournot game are given to confirm the effectiveness of our algorithm.