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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.18582 |
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| _version_ | 1866911968946814976 |
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| author | Yu, Lu |
| author_facet | Yu, Lu |
| contents | For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are not necessarily lattices, we generalize the Abian-Brown and the Markowsky fixed point theorems from single-valued maps to multivalued correspondences. We provide an application in game theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18582 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Order-theoretical fixed point theorems for correspondences and application in game theory Yu, Lu Theoretical Economics For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are not necessarily lattices, we generalize the Abian-Brown and the Markowsky fixed point theorems from single-valued maps to multivalued correspondences. We provide an application in game theory. |
| title | Order-theoretical fixed point theorems for correspondences and application in game theory |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2407.18582 |