Monotone Comparative Statics without Lattices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866915835988148224 |
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| author | Che, Yeon-Koo Kim, Jinwoo Kojima, Fuhito |
| author_facet | Che, Yeon-Koo Kim, Jinwoo Kojima, Fuhito |
| contents | The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multidimensional environments such as mixed-strategy games where this property fails. We show that this structure is not essential. We introduce a weaker notion, the pseudo-lattice property, and preserve the theory's core results by generalizing the MCS theorems for individual choice and Tarski's fixed-point theorem. Our framework expands comparative statics to pseudo quasi-supermodular games. Crucially, it enables the first MCS analysis of mixed-strategy Nash equilibria and trembling-hand perfect equilibria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_06442 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Monotone Comparative Statics without Lattices Che, Yeon-Koo Kim, Jinwoo Kojima, Fuhito Theoretical Economics Computer Science and Game Theory The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multidimensional environments such as mixed-strategy games where this property fails. We show that this structure is not essential. We introduce a weaker notion, the pseudo-lattice property, and preserve the theory's core results by generalizing the MCS theorems for individual choice and Tarski's fixed-point theorem. Our framework expands comparative statics to pseudo quasi-supermodular games. Crucially, it enables the first MCS analysis of mixed-strategy Nash equilibria and trembling-hand perfect equilibria. |
| title | Monotone Comparative Statics without Lattices |
| topic | Theoretical Economics Computer Science and Game Theory |
| url | https://arxiv.org/abs/1911.06442 |