A Linearly Convergent Distributed Nash Equilibrium Seeking Algorithm for Aggregative Games Over Time-Varying Unbalanced Graphs
针对时变不平衡通信图上的聚合博弈，提出一种分布式离散时间算法来求解纳什均衡，结合平均跟踪和推-和协议估计全局聚合量，并利用可行方向法处理集合约束，证明了线性收敛性。
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.