A distributed algorithm for average aggregative games with coupling constraints
It addresses the challenge of distributed decision-making in multi-agent systems with both cost and constraint couplings, which is relevant for networked control and economics.
The paper proposes a distributed algorithm for average aggregative games with coupling constraints, achieving an almost Nash equilibrium through local communications. The algorithm is applied to a multi-market Cournot game with transportation costs and maximum market capacity.
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.