The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space
The aim of this paper is to study some new stability results on the essential component and generic uniqueness of stationary equilibria for mean field games with finite state and action space (briefly, FSASMFG). A group of FSASMFGs comprises a dense residual subset such that every point of stationar...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/jofs/2619926 |
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| _version_ | 1849227081354838016 |
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| author | Luping Liu Wensheng Jia |
| author_facet | Luping Liu Wensheng Jia |
| author_sort | Luping Liu |
| collection | DOAJ |
| description | The aim of this paper is to study some new stability results on the essential component and generic uniqueness of stationary equilibria for mean field games with finite state and action space (briefly, FSASMFG). A group of FSASMFGs comprises a dense residual subset such that every point of stationary mean field equilibrium (briefly, SMFE) is essential. However, it is not true that any mapping has at least one essential fixed point; for example, the identity mapping of the interval [0, 1] onto itself has no essential fixed point. Thus, we further investigate that every FSASMFG has at least one essential component of its SMFE by proving the connectivity of minimal essential sets of the SMFE. Furthermore, we verify that, in the sense of Baire’s category, most FSASMFGs have a unique deterministic stationary equilibrium by means of nonlinear analysis and set-valued analysis. |
| format | Article |
| id | doaj-art-65aa3bc940e94ffea4b29a364d9b3a93 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-65aa3bc940e94ffea4b29a364d9b3a932025-08-24T00:00:01ZengWileyJournal of Function Spaces2314-88882025-01-01202510.1155/jofs/2619926The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action SpaceLuping Liu0Wensheng Jia1Computer and Information Engineering CollegeSchool of Mathematics and StatisticsThe aim of this paper is to study some new stability results on the essential component and generic uniqueness of stationary equilibria for mean field games with finite state and action space (briefly, FSASMFG). A group of FSASMFGs comprises a dense residual subset such that every point of stationary mean field equilibrium (briefly, SMFE) is essential. However, it is not true that any mapping has at least one essential fixed point; for example, the identity mapping of the interval [0, 1] onto itself has no essential fixed point. Thus, we further investigate that every FSASMFG has at least one essential component of its SMFE by proving the connectivity of minimal essential sets of the SMFE. Furthermore, we verify that, in the sense of Baire’s category, most FSASMFGs have a unique deterministic stationary equilibrium by means of nonlinear analysis and set-valued analysis.http://dx.doi.org/10.1155/jofs/2619926 |
| spellingShingle | Luping Liu Wensheng Jia The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space Journal of Function Spaces |
| title | The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space |
| title_full | The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space |
| title_fullStr | The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space |
| title_full_unstemmed | The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space |
| title_short | The Stability of Stationary Equilibria of Mean Field Games With Finite State and Action Space |
| title_sort | stability of stationary equilibria of mean field games with finite state and action space |
| url | http://dx.doi.org/10.1155/jofs/2619926 |
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