Convergence Analysis of Distributed Generalized Nash Equilibria Seeking Algorithm With Asynchrony and Delays

This article considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce a new local edge-based equilibrium condition with full in...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 70; no. 1; pp. 642 - 648
Main Authors: Li, Huaqing, Ran, Liang, Zheng, Lifeng, Li, Zhe, Hu, Jinhui, Li, Jun, Huang, Tingwen
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2025
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Asynchronous distributed algorithm
Convergence
delay communication
Delays
Distributed algorithms
Equilibrium conditions
Game theory
Games
generalized Nash equilibria (GNE)
Heuristic algorithms
noncooperative games
operator splitting
Vectors
ISSN:0018-9286, 1558-2523
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce a new local edge-based equilibrium condition with full information. Considering challenges when communication delays occur, we then devise an asynchronous distributed algorithm to seek a generalized Nash equilibrium. This asynchronous scheme arbitrarily activates one player to start new computations independently at different iteration instants, which means that the picked player can use the involved outdated information from itself and its neighbors to perform new updates. In theoretical aspect, we provide explicit conditions on algorithm parameters, for instance, the step-sizes to establish a sublinear convergence rate for the synchronous version. Next, the asynchronous algorithm guarantees almost sure convergence in expectation under the same step-size conditions and some standard assumptions. Finally, the viability and performance of the proposed algorithm are demonstrated by numerical studies on the Cournot competition.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2024.3439652