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Matching with Quotas

Author

Listed:
  • Mikhail Freer

    (Interdisciplinary Center for Economic Science and Department of Economics, George Mason University)

  • Mariia Titova

    (Department of Economics, University of California, San Diego)

Abstract

The paper characterizes the core of many-to-one matching problem with quotas. The many-to-one matching problem with quotas may have an empty core, and there is no clear set of necessary and sufficient conditions that guarantee non-emptiness of the core. Usual sufficient conditions for non-emptiness of the core for matching problems cannot be applied for the problem with quotas. We introduce set strong substitutability of preferences, a refinement of strong substitutability for the problem with quotas. We show that if preferences are set strongly substitutable, then the core of many-to-one matching problem with quotas is non-empty. Moreover, we prove that in this case the core has a lattice structure with opposition of interests. Length: 16

Suggested Citation

  • Mikhail Freer & Mariia Titova, 2015. "Matching with Quotas," Working Papers 1051, George Mason University, Interdisciplinary Center for Economic Science, revised Jul 2016.
    • Handle: RePEc:gms:wpaper:1051
    as

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    File URL: http://www.gmu.edu/schools/chss/economics/icesworkingpapers.gmu.edu/pdf/1051.pdf
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    References listed on IDEAS

    as
    1. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    2. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    3. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    5. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    6. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching; Stability; Fixed Point; Quotas;
    All these keywords.

    JEL classification:

    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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