Nash equilibrium seeking in N-coalition games via a gradient-free method
This paper studies an N-coalition non-cooperative game problem, where the players in the same coalition cooperatively minimize the sum of their local cost functions under a directed communication graph, while collectively acting as a virtual player to play a non-cooperative game with other coalition...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Online Access: | https://hdl.handle.net/10356/159373 |
| _version_ | 1826110797224345600 |
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| author | Pang, Yipeng Hu, Guoqiang |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Pang, Yipeng Hu, Guoqiang |
| author_sort | Pang, Yipeng |
| collection | NTU |
| description | This paper studies an N-coalition non-cooperative game problem, where the players in the same coalition cooperatively minimize the sum of their local cost functions under a directed communication graph, while collectively acting as a virtual player to play a non-cooperative game with other coalitions. Moreover, it is assumed that the players have no access to the explicit functional form but only the function value of their local costs. To solve the problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based on the gradient tracking method, is proposed. Specifically, a gradient estimator is developed locally based on Gaussian smoothing to estimate the partial gradients, and a gradient tracker is constructed locally to trace the average sum of the partial gradients among the players within the coalition. With a sufficiently small constant step-size, we show that all players’ actions approximately converge to the Nash equilibrium at a geometric rate under a strongly monotone game mapping condition. Numerical simulations are conducted to verify the effectiveness of the proposed algorithm. |
| first_indexed | 2024-10-01T02:40:22Z |
| format | Journal Article |
| id | ntu-10356/159373 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:40:22Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1593732022-06-16T05:25:13Z Nash equilibrium seeking in N-coalition games via a gradient-free method Pang, Yipeng Hu, Guoqiang School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Nash Equilibrium Seeking Gradient-Free Methods This paper studies an N-coalition non-cooperative game problem, where the players in the same coalition cooperatively minimize the sum of their local cost functions under a directed communication graph, while collectively acting as a virtual player to play a non-cooperative game with other coalitions. Moreover, it is assumed that the players have no access to the explicit functional form but only the function value of their local costs. To solve the problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based on the gradient tracking method, is proposed. Specifically, a gradient estimator is developed locally based on Gaussian smoothing to estimate the partial gradients, and a gradient tracker is constructed locally to trace the average sum of the partial gradients among the players within the coalition. With a sufficiently small constant step-size, we show that all players’ actions approximately converge to the Nash equilibrium at a geometric rate under a strongly monotone game mapping condition. Numerical simulations are conducted to verify the effectiveness of the proposed algorithm. Ministry of Education (MOE) This research was supported by Singapore Ministry of Education Academic Research Fund Tier 1 RG180/17(2017-T1-002-158). 2022-06-16T05:25:13Z 2022-06-16T05:25:13Z 2022 Journal Article Pang, Y. & Hu, G. (2022). Nash equilibrium seeking in N-coalition games via a gradient-free method. Automatica, 136, 110013-. https://dx.doi.org/10.1016/j.automatica.2021.110013 0005-1098 https://hdl.handle.net/10356/159373 10.1016/j.automatica.2021.110013 2-s2.0-85119404175 136 110013 en RG180/17(2017-T1-002-158) Automatica © 2021 Elsevier Ltd. All rights reserved. |
| spellingShingle | Engineering::Electrical and electronic engineering Nash Equilibrium Seeking Gradient-Free Methods Pang, Yipeng Hu, Guoqiang Nash equilibrium seeking in N-coalition games via a gradient-free method |
| title | Nash equilibrium seeking in N-coalition games via a gradient-free method |
| title_full | Nash equilibrium seeking in N-coalition games via a gradient-free method |
| title_fullStr | Nash equilibrium seeking in N-coalition games via a gradient-free method |
| title_full_unstemmed | Nash equilibrium seeking in N-coalition games via a gradient-free method |
| title_short | Nash equilibrium seeking in N-coalition games via a gradient-free method |
| title_sort | nash equilibrium seeking in n coalition games via a gradient free method |
| topic | Engineering::Electrical and electronic engineering Nash Equilibrium Seeking Gradient-Free Methods |
| url | https://hdl.handle.net/10356/159373 |
| work_keys_str_mv | AT pangyipeng nashequilibriumseekinginncoalitiongamesviaagradientfreemethod AT huguoqiang nashequilibriumseekinginncoalitiongamesviaagradientfreemethod |