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...

Full description

Bibliographic Details
Main Authors: Jingran Cheng, Menggang Chen, Huaqing Li, Yawei Shi, Zhongzheng Wang, Jialong Tang
Format: Article
Language:English
Published: MDPI AG 2023-06-01
Series:Applied Sciences
Subjects:
Online Access:https://www.mdpi.com/2076-3417/13/12/7058
_version_ 1797596228515528704
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.
first_indexed 2024-03-11T02:48:39Z
format Article
id doaj.art-51719039ffd348bbac47ce5fe7fb4ed8
institution Directory Open Access Journal
issn 2076-3417
language English
last_indexed 2024-03-11T02:48:39Z
publishDate 2023-06-01
publisher MDPI AG
record_format Article
series Applied Sciences
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
work_keys_str_mv AT jingrancheng distributedgneseekingunderglobaldecisionandpartialdecisioninformationoverdouglasrachfordsplittingmethod
AT menggangchen distributedgneseekingunderglobaldecisionandpartialdecisioninformationoverdouglasrachfordsplittingmethod
AT huaqingli distributedgneseekingunderglobaldecisionandpartialdecisioninformationoverdouglasrachfordsplittingmethod
AT yaweishi distributedgneseekingunderglobaldecisionandpartialdecisioninformationoverdouglasrachfordsplittingmethod
AT zhongzhengwang distributedgneseekingunderglobaldecisionandpartialdecisioninformationoverdouglasrachfordsplittingmethod
AT jialongtang distributedgneseekingunderglobaldecisionandpartialdecisioninformationoverdouglasrachfordsplittingmethod