Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method
This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector...
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MDPI AG
2023-06-01
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author | Jingran Cheng Menggang Chen Huaqing Li Yawei Shi Zhongzheng Wang Jialong Tang |
author_facet | Jingran Cheng Menggang Chen Huaqing Li Yawei Shi Zhongzheng Wang Jialong Tang |
author_sort | Jingran Cheng |
collection | DOAJ |
description | This paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector that minimizes the cost for each player. Unlike most of the existing algorithms for GNEP, which require full information exchange among all players, this paper considers a more realistic scenario where players can only communicate with a subset of players through a connectivity graph. The proposed algorithm enables each player to estimate the decisions of other players and update their own and others’ estimates through local communication with their neighbors. By introducing a network Lagrangian function and applying the Douglas-Rachford splitting method (DR), the GNEP is reformulated as a zero-finding problem. It is shown that the DR method can find the generalized Nash equilibrium (GNE) of the original problem under some mild conditions. |
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id | doaj.art-51719039ffd348bbac47ce5fe7fb4ed8 |
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issn | 2076-3417 |
language | English |
last_indexed | 2024-03-11T02:48:39Z |
publishDate | 2023-06-01 |
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spelling | doaj.art-51719039ffd348bbac47ce5fe7fb4ed82023-11-18T09:08:22ZengMDPI AGApplied Sciences2076-34172023-06-011312705810.3390/app13127058Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting MethodJingran Cheng0Menggang Chen1Huaqing Li2Yawei Shi3Zhongzheng Wang4Jialong Tang5Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaChongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, ChinaThis paper develops an algorithm for solving the generalized Nash equilibrium problem (GNEP) in non-cooperative games. The problem involves a set of players, each with a cost function that depends on their own decision as well as the decisions of other players. The goal is to find a decision vector that minimizes the cost for each player. Unlike most of the existing algorithms for GNEP, which require full information exchange among all players, this paper considers a more realistic scenario where players can only communicate with a subset of players through a connectivity graph. The proposed algorithm enables each player to estimate the decisions of other players and update their own and others’ estimates through local communication with their neighbors. By introducing a network Lagrangian function and applying the Douglas-Rachford splitting method (DR), the GNEP is reformulated as a zero-finding problem. It is shown that the DR method can find the generalized Nash equilibrium (GNE) of the original problem under some mild conditions.https://www.mdpi.com/2076-3417/13/12/7058generalized Nash equilibrium (GNE)Douglas-Rachfordglobal decision informationpartial decision information |
spellingShingle | Jingran Cheng Menggang Chen Huaqing Li Yawei Shi Zhongzheng Wang Jialong Tang Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method Applied Sciences generalized Nash equilibrium (GNE) Douglas-Rachford global decision information partial decision information |
title | Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method |
title_full | Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method |
title_fullStr | Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method |
title_full_unstemmed | Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method |
title_short | Distributed GNE Seeking under Global-Decision and Partial-Decision Information over Douglas-Rachford Splitting Method |
title_sort | distributed gne seeking under global decision and partial decision information over douglas rachford splitting method |
topic | generalized Nash equilibrium (GNE) Douglas-Rachford global decision information partial decision information |
url | https://www.mdpi.com/2076-3417/13/12/7058 |
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