IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v154y2025icp53-61.html

A direct proof of the short-side advantage in random matching markets

Author

Listed:
  • Mauras, Simon
  • Prałat, Paweł
  • Vetta, Adrian

Abstract

We study the stable matching problem under the random matching model where the preferences of the doctors and hospitals are sampled uniformly and independently at random. In a balanced market with n doctors and n hospitals, the doctor-proposing deferred-acceptance algorithm gives doctors an expected rank of order log⁡n for their partners and hospitals an expected rank of order nlog⁡n for their partners (Pittel, 1989; Wilson, 1972). This situation is reversed in an unbalanced market with n+1 doctors and n hospitals (Ashlagi et al., 2017), a phenomenon known as the short-side advantage. The current proofs (Ashlagi et al., 2017; Cai and Thomas, 2022) of this fact are indirect, counter-intuitively being based upon analyzing the hospital-proposing deferred-acceptance algorithm. In this paper we provide a direct proof of the short-side advantage, explicitly analyzing the doctor-proposing deferred-acceptance algorithm. Our proof sheds light on how and why the phenomenon arises.

Suggested Citation

  • Mauras, Simon & Prałat, Paweł & Vetta, Adrian, 2025. "A direct proof of the short-side advantage in random matching markets," Games and Economic Behavior, Elsevier, vol. 154(C), pages 53-61.
    • Handle: RePEc:eee:gamebe:v:154:y:2025:i:c:p:53-61
    DOI: 10.1016/j.geb.2025.08.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825625001186
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2025.08.013?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
    2. Holzman, Ron & Samet, Dov, 2014. "Matching of like rank and the size of the core in the marriage problem," Games and Economic Behavior, Elsevier, vol. 88(C), pages 277-285.
    3. Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    4. P'eter Bir'o & Avinatan Hassidim & Assaf Romm & Ran I. Shorrer & S'andor S'ov'ag'o, 2020. "The Large Core of College Admission Markets: Theory and Evidence," Papers 2010.08631, arXiv.org, revised Aug 2022.
    5. Rheingans-Yoo, Ross, 2024. "Large random matching markets with localized preference structures can exhibit large cores," Games and Economic Behavior, Elsevier, vol. 144(C), pages 71-83.
    6. Boris Pittel, 2019. "On Likely Solutions of the Stable Matching Problem with Unequal Numbers of Men and Women," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 122-146, February.
    7. Eduardo M. Azevedo & Jacob D. Leshno, 2016. "A Supply and Demand Framework for Two-Sided Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1235-1268.
    8. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    9. 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)

    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. Rheingans-Yoo, Ross, 2024. "Large random matching markets with localized preference structures can exhibit large cores," Games and Economic Behavior, Elsevier, vol. 144(C), pages 71-83.
    2. Kristian Koerselman, 2020. "Why Finnish polytechnics reject top applicants," Education Economics, Taylor & Francis Journals, vol. 28(5), pages 491-507, September.
    3. Itai Ashlagi & Mark Braverman & Amin Saberi & Clayton Thomas & Geng Zhao, 2020. "Tiered Random Matching Markets: Rank is Proportional to Popularity," Papers 2009.05124, arXiv.org, revised Jan 2021.
    4. Nick Arnosti, 2022. "A Continuum Model of Stable Matching With Finite Capacities," Papers 2205.12881, arXiv.org.
    5. Nick Arnosti, 2023. "Lottery Design for School Choice," Management Science, INFORMS, vol. 69(1), pages 244-259, January.
    6. Benjamin N. Roth & Ran I. Shorrer, 2021. "Making Marketplaces Safe: Dominant Individual Rationality and Applications to Market Design," Management Science, INFORMS, vol. 67(6), pages 3694-3713, June.
    7. Simon Mauras, 2020. "Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures," Papers 2005.08584, arXiv.org.
    8. Yusuke Narita, 2021. "A Theory of Quasi-Experimental Evaluation of School Quality," Management Science, INFORMS, vol. 67(8), pages 4982-5010, August.
    9. Saraiva, Gustavo, 2021. "An improved bound to manipulation in large stable matches," Games and Economic Behavior, Elsevier, vol. 129(C), pages 55-77.
    10. Marcelo Ariel Fernandez & Kirill Rudov & Leeat Yariv, 2022. "Centralized Matching with Incomplete Information," American Economic Review: Insights, American Economic Association, vol. 4(1), pages 18-33, March.
    11. Ortega, Josué, 2018. "Social integration in two-sided matching markets," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 119-126.
    12. Yusuke Narita, 2020. "A Theory of Quasi-Experimental Evaluation of School Quality," Working Papers 2020-085, Human Capital and Economic Opportunity Working Group.
    13. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
    14. Alvin E. Roth, 2024. "Market Design and Maintenance," NBER Chapters, in: New Directions in Market Design, pages 9-30, National Bureau of Economic Research, Inc.
    15. 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).
    16. Martin Van der Linden, 2019. "Deferred acceptance is minimally manipulable," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 609-645, June.
    17. Aaron L. Bodoh-Creed, 2020. "Optimizing for Distributional Goals in School Choice Problems," Management Science, INFORMS, vol. 66(8), pages 3657-3676, August.
    18. Ashlagi, Itai & Nikzad, Afshin & Romm, Assaf, 2019. "Assigning more students to their top choices: A comparison of tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 115(C), pages 167-187.
    19. Honarvar, Morteza & Kamali Shahdadi, Behrang, 2021. "Stability and immunity to capacity manipulation in large matching markets," Economics Letters, Elsevier, vol. 206(C).
    20. Itai Ashlagi & Mark Braverman & Yash Kanoria & Peng Shi, 2020. "Clearing Matching Markets Efficiently: Informative Signals and Match Recommendations," Management Science, INFORMS, vol. 66(5), pages 2163-2193, May.

    More about this item

    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:154:y:2025:i:c:p:53-61. 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.