The matching problem with linear transfers is equivalent to a hide-and-seek game
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915645794287616 |
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| author | Galichon, Alfred Jacquet, Antoine |
| author_facet | Galichon, Alfred Jacquet, Antoine |
| contents | Matching problems with linearly transferable utility (LTU) generalize the well-studied transferable utility (TU) case by relaxing the assumption that utility is transferred one-for-one within matched pairs. We show that LTU matching problems can be reframed as nonzero-sum games between two players, thus generalizing a result from von Neumann. The underlying linear programming structure of TU matching problems, however, is lost when moving to LTU. These results draw a new bridge between non-TU matching problems and the theory of bimatrix games, with consequences notably regarding the computation of stable outcomes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12200 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The matching problem with linear transfers is equivalent to a hide-and-seek game Galichon, Alfred Jacquet, Antoine Theoretical Economics Matching problems with linearly transferable utility (LTU) generalize the well-studied transferable utility (TU) case by relaxing the assumption that utility is transferred one-for-one within matched pairs. We show that LTU matching problems can be reframed as nonzero-sum games between two players, thus generalizing a result from von Neumann. The underlying linear programming structure of TU matching problems, however, is lost when moving to LTU. These results draw a new bridge between non-TU matching problems and the theory of bimatrix games, with consequences notably regarding the computation of stable outcomes. |
| title | The matching problem with linear transfers is equivalent to a hide-and-seek game |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2402.12200 |