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Unique Stable Matchings

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  • Gregory Z. Gutin
  • Philip R. Neary
  • Anders Yeo

Abstract

In this paper we consider the issue of a unique prediction in one to one two sided matching markets, as defined by Gale and Shapley (1962), and we prove the following. Theorem. Let P be a one-to-one two-sided matching market and let P be its associated normal form, a (weakly) smaller matching market with the same set of stable matchings, that can be obtained using procedures introduced in Irving and Leather (1986) and Balinski and Ratier (1997). The following three statements are equivalent (a) P has a unique stable matching. (b) Preferences on P* are acyclic, as defined by Chung (2000). (c) In P* every market participant's preference list is a singleton.

Suggested Citation

  • Gregory Z. Gutin & Philip R. Neary & Anders Yeo, 2021. "Unique Stable Matchings," Papers 2106.12977, arXiv.org, revised Jul 2023.
    • Handle: RePEc:arx:papers:2106.12977
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    References listed on IDEAS

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    Cited by:

    1. Estelle Cantillon & Li Chen & Juan Sebastian Pereyra Barreiro, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?," Working Papers ECARES 2022-39, ULB -- Universite Libre de Bruxelles.
    2. Gregory Gutin & Philip R. Neary & Anders Yeo, 2022. "Finding all stable matchings with assignment constraints," Papers 2204.03989, arXiv.org, revised Oct 2023.
    3. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2024. "Stable matching as transportation," Papers 2402.13378, arXiv.org.

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