  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 constraints coupling their
strategies. We propose a distributed algorithm that achieves an almost 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 and exploits a novel
result of parametric convergence of variational inequalities, which is
applicable beyond the context of games. We apply our theoretical findings to a
multi-market Cournot game with transportation costs and maximum market
capacity.
