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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2408.14433 |
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| _version_ | 1866929474893774848 |
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| author | Bao, Nguyen Xuan Duy Mordukhovich, Boris Nam, Nguyen Mau |
| author_facet | Bao, Nguyen Xuan Duy Mordukhovich, Boris Nam, Nguyen Mau |
| contents | In this paper, we first provide a simple variational proof of the existence of Nash equilibrium in Hilbert spaces by using optimality conditions in convex minimization and Schauder's fixed-point theorem. Then applications of convex analysis and generalized differentiation are given to the existence of Nash equilibrium and extended versions of von Neumann's minimax theorem in locally convex topological vector spaces. Our analysis in this part combines generalized differential tools of convex analysis with elements of fixed point theory revolving around Kakutani's fixed-point theorem and related issues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nash Equilibrium and Minimax Theorems via Variational Tools of Convex Analysis Bao, Nguyen Xuan Duy Mordukhovich, Boris Nam, Nguyen Mau Optimization and Control In this paper, we first provide a simple variational proof of the existence of Nash equilibrium in Hilbert spaces by using optimality conditions in convex minimization and Schauder's fixed-point theorem. Then applications of convex analysis and generalized differentiation are given to the existence of Nash equilibrium and extended versions of von Neumann's minimax theorem in locally convex topological vector spaces. Our analysis in this part combines generalized differential tools of convex analysis with elements of fixed point theory revolving around Kakutani's fixed-point theorem and related issues. |
| title | Nash Equilibrium and Minimax Theorems via Variational Tools of Convex Analysis |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2408.14433 |