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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18539 |
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| _version_ | 1866917734416121856 |
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| author | Sultana, Asrifa Valecha, Shivani |
| author_facet | Sultana, Asrifa Valecha, Shivani |
| contents | We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions under which an equilibrium for the generalized game can be obtained by solving a quasi-variational inequality. Based on this variational reformulation, we derive the existence of equilibrium for generalized games with non-ordered (that is, associated weak preference relations need not be complete and transitive) and mid-point continuous preference maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18539 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational Analysis of Generalized Games over Banach spaces Sultana, Asrifa Valecha, Shivani Optimization and Control Functional Analysis 49J40, 49J53, 91B06, 91B42 We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions under which an equilibrium for the generalized game can be obtained by solving a quasi-variational inequality. Based on this variational reformulation, we derive the existence of equilibrium for generalized games with non-ordered (that is, associated weak preference relations need not be complete and transitive) and mid-point continuous preference maps. |
| title | Variational Analysis of Generalized Games over Banach spaces |
| topic | Optimization and Control Functional Analysis 49J40, 49J53, 91B06, 91B42 |
| url | https://arxiv.org/abs/2407.18539 |