A Distributed Algorithm For Almost-Nash Equilibria of Average Aggregative Games With Coupling Constraints

We consider the framework of average aggregative games, where the cost function of each agent depends on his own strategy and on the average population strategy. We focus on the case in which the agents are coupled not only via their cost functions, but also via a shared constraint coupling their strategies. We propose a distributed algorithm that achieves an $\varepsilon$-Nash equilibrium by requiring only local communications of the agents, as specified by a sparse communication network. The proof of convergence of the algorithm relies on the auxiliary class of network aggregative games. We apply our theoretical findings to a multimarket Cournot game with transportation costs and maximum market capacity.