Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method

This article considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the...

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Main Authors: Pang, Yipeng, Hu, Guoqiang
Other Authors: School of Electrical and Electronic Engineering
Format: Article
Language:English
Published: 2022
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Online Access:https://hdl.handle.net/10356/159486
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1594862022-06-21T08:24:34Z Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method Pang, Yipeng Hu, Guoqiang School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Distributed Algorithms Game Theory This article considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the problem, a leader-following consensus gradient-free distributed Nash equilibrium seeking algorithm is proposed. This algorithm utilizes only the measurements of the player' local cost function without the knowledge of its explicit expression or the requirement on its smoothness. Hence, the algorithm is gradient-free during the entire updating process. Moreover, the analysis on the convergence of the Nash equilibrium is studied for the algorithm with both diminishing and constant step-sizes, respectively. Specifically, in the case of diminishing step-size, it is shown that the players' actions converge to the Nash equilibrium almost surely, while in the case of fixed step-size, the convergence to the neighborhood of the Nash equilibrium is achieved. The performance of the proposed algorithm is verified through numerical simulations. Building and Construction Authority (BCA) Ministry of Education (MOE) National Research Foundation (NRF) This work was supported in part by Singapore Ministry of Education Academic Research Fund under Grant Tier 1 RG180/17(2017-T1-002- 158), and in part by the National Research Foundation, Prime Minister’s Office, Singapore under the Energy Innovation Research Programme (EIRP) for Building Energy Efficiency Grant Call under Grant NRF2013EWT-EIRP004-051, administered by the Building and Construction Authority. 2022-06-21T08:24:34Z 2022-06-21T08:24:34Z 2021 Journal Article Pang, Y. & Hu, G. (2021). Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method. IEEE Transactions On Automatic Control, 66(4), 1832-1839. https://dx.doi.org/10.1109/TAC.2020.2995666 0018-9286 https://hdl.handle.net/10356/159486 10.1109/TAC.2020.2995666 2-s2.0-85103437076 4 66 1832 1839 en RG180/17(2017-T1-002- 158) NRF2013EWT-EIRP004-051 IEEE Transactions on Automatic Control © 2020 IEEE. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Electrical and electronic engineering
Distributed Algorithms
Game Theory
spellingShingle Engineering::Electrical and electronic engineering
Distributed Algorithms
Game Theory
Pang, Yipeng
Hu, Guoqiang
Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
description This article considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the problem, a leader-following consensus gradient-free distributed Nash equilibrium seeking algorithm is proposed. This algorithm utilizes only the measurements of the player' local cost function without the knowledge of its explicit expression or the requirement on its smoothness. Hence, the algorithm is gradient-free during the entire updating process. Moreover, the analysis on the convergence of the Nash equilibrium is studied for the algorithm with both diminishing and constant step-sizes, respectively. Specifically, in the case of diminishing step-size, it is shown that the players' actions converge to the Nash equilibrium almost surely, while in the case of fixed step-size, the convergence to the neighborhood of the Nash equilibrium is achieved. The performance of the proposed algorithm is verified through numerical simulations.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Pang, Yipeng
Hu, Guoqiang
format Article
author Pang, Yipeng
Hu, Guoqiang
author_sort Pang, Yipeng
title Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
title_short Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
title_full Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
title_fullStr Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
title_full_unstemmed Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
title_sort distributed nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method
publishDate 2022
url https://hdl.handle.net/10356/159486
_version_ 1736856397611532288