An incentive mechanism for agents playing competitive aggregative games

We propose an incentive mechanism for steering the strategies of noncooperative heterogeneous agents, each with strongly convex cost function depend- ing on the average among the agents’ strategies, and all sharing a convex constraint, toward a competitive aggregative equilibrium. We consider a co- ordinator agent having access to the average among the agents’ strategies and broadcasting incentive signals that affect the decentralized optimal responses of the agents. Our mechanism ensures, based on the Picard–Banach fixed point iteration, global convergence to an equilibrium.