A distributed primal-dual algorithm for computation of generalized Nash equilibria via operator splitting methods

In this paper, we propose a distributed algorithm for computation of a generalized Nash equilibrium (GNE) in noncooperative games over networks. We consider games in which the feasible decision sets of all players are coupled together by a globally shared affine constraint. Adopting the variational GNE as a refined solution, we reformulate the problem as that of finding the zeros of a sum of monotone operators through a primal-dual analysis and an augmentation of variables. Then we introduce a distributed algorithm based on forward-backward operator splitting methods. Each player only needs to know its local objective function, local feasible set, and a local block of the affine constraint, and share information with its neighbours. We show convergence of the proposed algorithm for fixed step-sizes. Numerical simulations are given for networked Cournot competition with bounded market capacities.