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A class of multipartner matching markets with a strong lattice structure

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  • Ahmet Alkan

    ()
    (Sabanci University, 81474 Tuzla, Istanbul, TURKEY)

Abstract

For a two-sided multipartner matching model where agents are given by path-independent choice functions and no quota restrictions, Blair [7] had shown that stable matchings always exist and form a lattice. However, the lattice operations were not simple and not distributive. Recently Alkan [3] showed that if one introduces quotas together with a monotonicity condition then the set of stable matchings is a distributive lattice under a natural definition of supremum and infimum for matchings. In this study we show that the quota restriction can be removed and replaced by a more general condition named cardinal monotonicity and all the structural properties derived in [3] still hold. In particular, although there are no exogenous quotas in the model there is endogenously a sort of quota; more precisely, each agent has the same number of partners in every stable matching. Stable matchings also have the polarity property (supremum with respect to one side is identical to infimum with respect to the other side) and a property we call {\it complementarity}.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 19 (2002)
Issue (Month): 4 ()
Pages: 737-746

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Handle: RePEc:spr:joecth:v:19:y:2002:i:4:p:737-746

Note: Received: May 5, 2000; revised version: January 25, 2001
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Related research

Keywords: Stable matchings; Revealed preference; Path independent choice function; Lattice; Two-sided market.;

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Cited by:
  1. Scott Duke Kominers & Tayfun Sönmez, 2012. "Designing for Diversity: Matching with Slot-Specific Priorities," Boston College Working Papers in Economics 806, Boston College Department of Economics.
  2. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
  3. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
  4. Flip Klijn, 2011. "A Many-to-Many 'Rural Hospital Theorem'," UFAE and IAE Working Papers 877.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Orhan Aygün & Tayfun Sönmez, 2012. "Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts," Boston College Working Papers in Economics 804, Boston College Department of Economics.
  6. Paula Jaramillo & Kagi Cagatay & Flip Klijn, 2012. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," DOCUMENTOS DE TRABAJO 009997, UNIVERSIDAD DEL ROSARIO.
  7. Chen, Ning & Li, Mengling, 2013. "Ties matter: improving efficiency in course allocation by introducing ties," MPRA Paper 47031, University Library of Munich, Germany.
  8. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics 805, Boston College Department of Economics.
  9. David Cantala, 2011. "Agreement toward stability in matching markets," Review of Economic Design, Springer, vol. 15(4), pages 293-316, December.

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