An operator splitting approach for distributed generalized Nash equilibria computation

Abstract 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. However, each player also needs to observe the decisions that its objective function directly depends on to evaluate its local gradient. We show convergence of the proposed algorithm for fixed step-sizes under some mild assumptions. Moreover, a distributed algorithm with inertia is also introduced and analysed for distributed variational GNE seeking. Numerical simulations are given for networked Cournot competition with bounded market capacities, to illustrate the algorithm efficiency and performance.

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