IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2407.19831.html

The Large and Likely Inefficiency of Stable Matching Mechanisms

Author

Listed:
  • Josue Ortega
  • Gabriel Ziegler
  • R. Pablo Arribillaga
  • Geng Zhao

Abstract

We prove that any stable matching mechanism suffers from systematic inefficiency of striking magnitude: in large random markets, any stable allocation is Pareto-inefficient with high probability, and almost all students can simultaneously improve their placements without harming anyone else. We establish this result by showing that the envy digraph generated by the student-proposing Deferred Acceptance mechanism contains a unique giant strongly connected component, implying that nearly all students are improvable via trading cycles. Finally, we show that every maximal cycle packing covers almost all students, revealing a surprising asymptotic equivalence among all efficient mechanisms that Pareto-dominate DA.

Suggested Citation

  • Josue Ortega & Gabriel Ziegler & R. Pablo Arribillaga & Geng Zhao, 2024. "The Large and Likely Inefficiency of Stable Matching Mechanisms," Papers 2407.19831, arXiv.org, revised Jul 2026.
    • Handle: RePEc:arx:papers:2407.19831
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2407.19831
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alfred Galichon & Octavia Ghelfi & Marc Henry, 2021. "Stable and Extremely Unequal," Sciences Po Economics Publications (main) hal-03936184, HAL.
    2. Galichon, Alfred & Ghelfi, Octavia & Henry, Marc, 2023. "Stable and extremely unequal," Economics Letters, Elsevier, vol. 226(C).
    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. Afacan, Mustafa Oğuz & Dur, Umut, 2024. "Rawlsian Matching," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 101-106.
    2. Josue Ortega & Gabriel Ziegler & R. Pablo Arribillaga & Geng Zhao, 2025. "What Pareto-Efficiency Adjustments Cannot Fix," Papers 2506.11660, arXiv.org.
    3. Ortega, Josué & Ziegler, Gabriel & Arribillaga, R. Pablo, 2024. "Unimprovable Students and Inequality in School Choice," QBS Working Paper Series 2024/05, Queen's University Belfast, Queen's Business School.
    4. Ortega, Josué & Klein, Thilo, 2023. "The cost of strategy-proofness in school choice," Games and Economic Behavior, Elsevier, vol. 141(C), pages 515-528.
    5. Juan Pereyra & Tom Demeulemeester, 2024. "Rawlsian Assignments," Documentos de Trabajo/Working Papers 2403, Facultad de Ciencias Empresariales y Economia. Universidad de Montevideo..
    6. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2024. "Stable Matching as Transport: a Welfarist Perspective on Market Design," Papers 2402.13378, arXiv.org, revised Jun 2026.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2407.19831. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.