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...

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Vydané v:	IEEE transactions on automatic control Ročník 70; číslo 1; s. 642 - 648
Hlavní autori:	Li, Huaqing, Ran, Liang, Zheng, Lifeng, Li, Zhe, Hu, Jinhui, Li, Jun, Huang, Tingwen
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York IEEE 01.01.2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
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Abstract	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new computations independently at different iteration instants, which means that the picked player can use the involved outdated information from itself and its neighbors to perform new updates.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.
AbstractList	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.
Author	Li, Jun Huang, Tingwen Li, Huaqing Li, Zhe Hu, Jinhui Ran, Liang Zheng, Lifeng
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SubjectTerms	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
Title	Convergence Analysis of Distributed Generalized Nash Equilibria Seeking Algorithm With Asynchrony and Delays
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