On Smithson's fixed point theorem for order preserving multifunctions
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866908836851351552 |
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| author | Kono, Haruki Voorneveld, Mark |
| author_facet | Kono, Haruki Voorneveld, Mark |
| contents | Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains why Smithson's argument is invalid. It also contains new results on the structure of the set of fixed points and monotone comparative statics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15483 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Smithson's fixed point theorem for order preserving multifunctions Kono, Haruki Voorneveld, Mark Combinatorics Theoretical Economics Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains why Smithson's argument is invalid. It also contains new results on the structure of the set of fixed points and monotone comparative statics. |
| title | On Smithson's fixed point theorem for order preserving multifunctions |
| topic | Combinatorics Theoretical Economics |
| url | https://arxiv.org/abs/2303.15483 |