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Matching through institutions

Author

Listed:
  • Francis Bloch

    (Université Paris 1 and Paris School of Economics)

  • David Cantala

    (El Colegio de México)

  • Damián Gibaja

    (Universidad Popular Autónoma del Estado de Puebla)

Abstract

We model a matching market with institutions -inspired by the assignment of social housing in Paris- as a three-sided market. Institutions own objects and have agents attached to them. Agents have preferences over objects. Objects have priorities over institutions. We show that fair assignments satisfying distributional constraints may fail to exist, and propose a sufficient condition -the over-demand condition- under which we prove existence. Existence derives from the construction of a new algorithm, the Nested Deferred Acceptance (NDA) algorithm, which combines a one-to-one matching between agents and objects and a one-to-many matching between objects and institutions. If interrupters are eliminated from the preference list, as in Kesten (2010), the NDA algorithm produces an assignment which is fair, Pareto optimal among fair assignments and strategy-proof for agents.

Suggested Citation

  • Francis Bloch & David Cantala & Damián Gibaja, 2017. "Matching through institutions," Serie documentos de trabajo del Centro de Estudios Económicos 2017-03, El Colegio de México, Centro de Estudios Económicos.
    • Handle: RePEc:emx:ceedoc:2017-03
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    File URL: https://cee.colmex.mx/dts/2017/DT-2017-3.pdf
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    References listed on IDEAS

    as
    1. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
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    10. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
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    13. 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.
    14. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
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    16. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    17. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    18. Masahiro Goto & Fuhito Kojima & Ryoji Kurata & Akihisa Tamura & Makoto Yokoo, 2017. "Designing Matching Mechanisms under General Distributional Constraints," American Economic Journal: Microeconomics, American Economic Association, vol. 9(2), pages 226-262, May.
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    Cited by:

    1. P'eter Bir'o & M'arton Gyetvai, 2021. "Online voluntary mentoring: Optimising the assignment of students and mentors," Papers 2102.06671, arXiv.org.
    2. Jorge Arenas & Juan Pablo Torres-Martinez, 2024. "On Incentives in Three-Sided Markets," Working Papers wp558, University of Chile, Department of Economics.
    3. Biró, Péter & Gyetvai, Márton, 2023. "Online voluntary mentoring: Optimising the assignment of students and mentors," European Journal of Operational Research, Elsevier, vol. 307(1), pages 392-405.

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    More about this item

    Keywords

    matching; institutions; deferred acceptance algorithm; social housing;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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