Methods for Solving Generalized Nash Equilibrium
The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash equilibrium problem (NEP), in which each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation o...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/762165 |
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| _version_ | 1832562350359576576 |
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| author | Biao Qu Jing Zhao |
| author_facet | Biao Qu Jing Zhao |
| author_sort | Biao Qu |
| collection | DOAJ |
| description | The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash equilibrium problem (NEP), in which each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido-Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP. |
| format | Article |
| id | doaj-art-2a91cbebbbb84209bd8b6ce714a0131a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2a91cbebbbb84209bd8b6ce714a0131a2025-02-03T01:22:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/762165762165Methods for Solving Generalized Nash EquilibriumBiao Qu0Jing Zhao1School of Management, Qufu Normal University, Rizhao, Shandong 276826, ChinaSchool of Management, Qufu Normal University, Rizhao, Shandong 276826, ChinaThe generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash equilibrium problem (NEP), in which each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido-Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP.http://dx.doi.org/10.1155/2013/762165 |
| spellingShingle | Biao Qu Jing Zhao Methods for Solving Generalized Nash Equilibrium Journal of Applied Mathematics |
| title | Methods for Solving Generalized Nash Equilibrium |
| title_full | Methods for Solving Generalized Nash Equilibrium |
| title_fullStr | Methods for Solving Generalized Nash Equilibrium |
| title_full_unstemmed | Methods for Solving Generalized Nash Equilibrium |
| title_short | Methods for Solving Generalized Nash Equilibrium |
| title_sort | methods for solving generalized nash equilibrium |
| url | http://dx.doi.org/10.1155/2013/762165 |
| work_keys_str_mv | AT biaoqu methodsforsolvinggeneralizednashequilibrium AT jingzhao methodsforsolvinggeneralizednashequilibrium |