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A decomposition from a substitutable many-to-one matching market to a one-to-one matching market

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  • Pablo Neme
  • Jorge Oviedo

Abstract

For a many-to-one market with substitutable preferences on the firm's side, based on the Aizerman-Malishevski decomposition, we define an associated one-to-one market. Given that the usual notion of stability for a one-to-one market does not fit well for this associated one-to-one market, we introduce a new notion of stability. This notion allows us to establish an isomorphism between the set of stable matchings in the many-to-one market and the matchings in the associated one-to-one market that meet this new stability criterion. Furthermore, we present an adaptation of the well-known deferred acceptance algorithm to compute a matching that satisfies this new notion of stability for the associated one-to-one market.

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  • Pablo Neme & Jorge Oviedo, 2024. "A decomposition from a substitutable many-to-one matching market to a one-to-one matching market," Papers 2411.00564, arXiv.org.
    • Handle: RePEc:arx:papers:2411.00564
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    References listed on IDEAS

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    1. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    2. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
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