IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v121y2020icp204-231.html
   My bibliography  Save this article

Matching through institutions

Author

Listed:
  • Bloch, Francis
  • Cantala, David
  • Gibaja, Damián

Abstract

We analyze a three-sided matching market where institutions own objects and individuals belong to institutions. Institutions pool their objects to enlarge the choice set of individuals. For any institution, the number of individuals who receive an object must be equal to the number of objects initially owned. Under this distributional constraint, individually rational and fair assignments may fail to exist. However, when the number of individuals is sufficiently large, fair assignments exist and can be found using a new algorithm, called the Nested Deferred Acceptance algorithm with interrupters (NDAI). This procedure nests a one-to-one matching between agents and objects and a one-to-many matching between objects and institutions. We show that it outputs a matching which is Pareto optimal among fair matchings and strategy-proof for individuals. When agents belong to several institutions, the NDAI results in assignments which are fair for agents of the same institution.

Suggested Citation

  • Bloch, Francis & Cantala, David & Gibaja, Damián, 2020. "Matching through institutions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 204-231.
    • Handle: RePEc:eee:gamebe:v:121:y:2020:i:c:p:204-231
    DOI: 10.1016/j.geb.2020.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825620300117
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2020.01.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    4. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    5. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    6. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
    7. Kojima, Fuhito, 2012. "School choice: Impossibilities for affirmative action," Games and Economic Behavior, Elsevier, vol. 75(2), pages 685-693.
    8. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    9. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    10. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    11. Umut Mert Dur & M. Utku Ünver, 2019. "Two-Sided Matching via Balanced Exchange," Journal of Political Economy, University of Chicago Press, vol. 127(3), pages 1156-1177.
    12. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    13. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
    14. Thành Nguyen & Rakesh Vohra, 2018. "Near-Feasible Stable Matchings with Couples," American Economic Review, American Economic Association, vol. 108(11), pages 3154-3169, November.
    15. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    16. Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Jorge Arenas & Juan Pablo Torres-Martinez, 2024. "On Incentives in Three-Sided Markets," Working Papers wp558, University of Chile, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    2. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    3. Tomoeda, Kentaro, 2018. "Finding a stable matching under type-specific minimum quotas," Journal of Economic Theory, Elsevier, vol. 176(C), pages 81-117.
    4. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202103100800001123, Iowa State University, Department of Economics.
    5. Avataneo, Michelle & Turhan, Bertan, 2021. "Slot-specific priorities with capacity transfers," Games and Economic Behavior, Elsevier, vol. 129(C), pages 536-548.
    6. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).
    7. Hafalir, Isa E. & Kojima, Fuhito & Yenmez, M. Bumin, 2022. "Interdistrict school choice: A theory of student assignment," Journal of Economic Theory, Elsevier, vol. 201(C).
    8. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202104130700001123, Iowa State University, Department of Economics.
    9. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    10. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    11. Orhan Aygun & Bertan Turhan, 2020. "Designing Direct Matching Mechanism for India with Comprehensive Affirmative Action," Papers 2004.13264, arXiv.org, revised Dec 2021.
    12. Orhan Aygün & Bertan Turhan, 2023. "How to De-Reserve Reserves: Admissions to Technical Colleges in India," Management Science, INFORMS, vol. 69(10), pages 6147-6164, October.
    13. Oguzhan Celebi, 2023. "Diversity Preferences, Affirmative Action and Choice Rules," Papers 2310.14442, arXiv.org.
    14. Doğan, Battal, 2016. "Responsive affirmative action in school choice," Journal of Economic Theory, Elsevier, vol. 165(C), pages 69-105.
    15. Umut Dur & Parag A. Pathak & Tayfun Sönmez, 2016. "Explicit vs. Statistical Preferential Treatment in Affirmative Action: Theory and Evidence from Chicago's Exam Schools," NBER Working Papers 22109, National Bureau of Economic Research, Inc.
    16. Braun, Sebastian & Dwenger, Nadja & Kübler, Dorothea & Westkamp, Alexander, 2014. "Implementing quotas in university admissions: An experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 232-251.
    17. Duddy, Conal, 2017. "The structure of priority in the school choice problem," MPRA Paper 81057, University Library of Munich, Germany.
    18. Abdulkadiroglu, Atila & Andersson, Tommy, 2022. "School Choice," Working Papers 2022:4, Lund University, Department of Economics.
    19. Jiao, Zhenhua & Shen, Ziyang, 2021. "School choice with priority-based affirmative action: A responsive solution," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 1-9.
    20. Tayfun Sönmez & M. Bumin Yenmez, 2019. "Can Economic Theory be Informative for the Judiciary? Affirmative Action in India via Vertical and Horizontal Reservations," Boston College Working Papers in Economics 1026, Boston College Department of Economics, revised 23 Jun 2021.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:121:y:2020:i:c:p:204-231. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.