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A class of multipartner matching markets with a strong lattice structure

Author

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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}.

Suggested Citation

  • 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.
  • 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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    Citations

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    Cited by:

    1. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    2. Bó, Inácio, 2016. "Fair implementation of diversity in school choice," Games and Economic Behavior, Elsevier, vol. 97(C), pages 54-63.
    3. Chen, Peter & Egesdal, Michael & Pycia, Marek & Yenmez, M. Bumin, 2016. "Median stable matchings in two-sided markets," Games and Economic Behavior, Elsevier, vol. 97(C), pages 64-69.
    4. M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    5. Chen, Ning & Li, Mengling, 2013. "Ties matter: improving efficiency in course allocation by introducing ties," MPRA Paper 47031, University Library of Munich, Germany.
    6. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    7. 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.
    8. David Cantala, 2011. "Agreement toward stability in matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 293-316, December.
    9. 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.
    10. 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.
    11. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    12. Mustafa Oǧuz Afacan, 2016. "Characterizations of the cumulative offer process," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 531-542, October.
    13. Bando, Keisuke, 2014. "On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm," Games and Economic Behavior, Elsevier, vol. 87(C), pages 269-287.
    14. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    15. repec:jmi:articl:jmi-v1i1a5 is not listed on IDEAS
    16. repec:eee:ecolet:v:156:y:2017:i:c:p:65-67 is not listed on IDEAS
    17. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2016. "Manipulability of Stable Mechanisms," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 202-214, May.
    18. repec:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-015-0525-3 is not listed on IDEAS
    19. Afacan, Mustafa Oǧuz, 2016. "Enrollment manipulations in school choice," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 119-125.
    20. 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.
    21. Afacan, Mustafa Oǧuz & Turhan, Bertan, 2015. "On relationships between substitutes conditions," Economics Letters, Elsevier, vol. 126(C), pages 10-12.
    22. Tam'as Fleiner & Zsuzsanna Jank'o & Akihisa Tamura & Alexander Teytelboym, 2015. "Trading Networks with Bilateral Contracts," Papers 1510.01210, arXiv.org, revised Feb 2016.
    23. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D49 - Microeconomics - - Market Structure, Pricing, and Design - - - Other

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