Fragile Stable Matchings
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911801533267968 |
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| author | Rudov, Kirill |
| author_facet | Rudov, Kirill |
| contents | We show how fragile stable matchings are in a decentralized one-to-one matching setting. The classical work of Roth and Vande Vate (1990) suggests simple decentralized dynamics in which randomly-chosen blocking pairs match successively. Such decentralized interactions guarantee convergence to a stable matching. Our first theorem shows that, under mild conditions, any unstable matching -- including a small perturbation of a stable matching -- can culminate in any stable matching through these dynamics. Our second theorem highlights another aspect of fragility: stabilization may take a long time. Even in markets with a unique stable matching, where the dynamics always converge to the same matching, decentralized interactions can require an exponentially long duration to converge. A small perturbation of a stable matching may lead the market away from stability and involve a sizable proportion of mismatched participants for extended periods. Our results hold for a broad class of dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fragile Stable Matchings Rudov, Kirill Theoretical Economics Computer Science and Game Theory We show how fragile stable matchings are in a decentralized one-to-one matching setting. The classical work of Roth and Vande Vate (1990) suggests simple decentralized dynamics in which randomly-chosen blocking pairs match successively. Such decentralized interactions guarantee convergence to a stable matching. Our first theorem shows that, under mild conditions, any unstable matching -- including a small perturbation of a stable matching -- can culminate in any stable matching through these dynamics. Our second theorem highlights another aspect of fragility: stabilization may take a long time. Even in markets with a unique stable matching, where the dynamics always converge to the same matching, decentralized interactions can require an exponentially long duration to converge. A small perturbation of a stable matching may lead the market away from stability and involve a sizable proportion of mismatched participants for extended periods. Our results hold for a broad class of dynamics. |
| title | Fragile Stable Matchings |
| topic | Theoretical Economics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2403.12183 |