Leader-Follower Network Aggregative Game with Stochastic Agents' Communication and Activeness

Abstract: This technical note presents a leader-follower scheme for network aggregative games. The followers and leader are selfish cost minimizing agents. The cost function of each follower is affected by strategy of leader and aggregated strategies of its neighbors through a communication graph. The leader infinitely often wakes up and receives the aggregated strategy of the followers, updates its decision value and broadcasts it to all the followers. Then, the followers apply the updated strategy of the leader into their cost functions. The establishment of information exchange between each neighboring pair of followers, and the activeness of each follower to update its decision at each iteration are both considered to be drawn from two arbitrary distributions. Moreover, a distributed algorithm based on subgradient method is proposed for updating the strategies of leader and followers. The convergence of the proposed algorithm to the unique generalized Nash equilibrium point of the game is proven in both almost sure and mean square senses.