An operator splitting approach for distributed generalized Nash equilibria computation

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...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 102; pp. 111 - 121
Main Authors: Yi, Peng, Pavel, Lacra
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.04.2019
Subjects:
Distributed algorithm
Generalized Nash equilibrium
Multi-agent systems
Operator splitting
Operator splitting
Generalized Nash equilibrium
Distributed algorithm
Multi-agent systems
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2019.01.008