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.

Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints

“…The designed strategy-updating rule mainly has three parts including the strategy update (8), the coordination of Lagrange multiplier (9) and the aggregator estimation (10). The former two parts are slow systems and the later one is a fast system, and they imply that the designed rule is executed in two timescales.…”

“…It is feasible to design α and ε for the strategies of all agents to reach the GNE of game G = (I, Ω, J). 8), (9), and ( 10) can be written as…”

“…Some algorithms based on best response dynamics were applied in the demand-response scheme of smart grids [6] and the spectrum sharing in communication networks [7]. The other algorithms based on gradient dynamics were applied to the networked Cournot competition [8] and power allocation of small cell networks [9]. Furthermore, there have been reports about aggregative games of high-order dynamical systems recently.…”

Achieving Social Optimum in Non-convex Cooperative Aggregative Games: A Distributed Stochastic Annealing Approach

“…The more complex case is to study Nash equilibriua of uncoopererative games, whose agents' local functions depend on agents' own decision variables but also other agents' decision variables. For example, in [26], algorithms were designed for the best-response schemes of uncooperative stochastic games while in [27], [28] were designed for uncooperative aggregative games. The aforementioned stochastic algorithms were mainly designed for solving problems with uncertain function information or communication topology between agents.…”

“…The above facts motivated this paper to study social optimum of non-convex cooperative aggregative games. Challenges mainly come from the more complex non-convex coopereative game setting, for which [27], [28] is not suitable. As mentioned before, stochastic annealing algorithms [31], [32] are efficient to deal with non-convex functions.…”