IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2507.07501.html
   My bibliography  Save this paper

Stability in Many-to-One Matching with Couples having Responsive Preferences

Author

Listed:
  • Shashwat Khare
  • Souvik Roy
  • Ton Storcken

Abstract

This paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. First, we show by means of an example that a stable matching may fail to exist even when both couples and institutions have responsive preferences. Next, we provide conditions on couples' preferences that are necessary and sufficient to ensure a stable matching for every preference profile where institutions may have any responsive preference. Finally, we do the same with respect to institutions' preferences, that is, we provide conditions on institutions' preferences that are necessary and sufficient to ensure a stable matching for every preference profile where couples may have any responsive preference.

Suggested Citation

  • Shashwat Khare & Souvik Roy & Ton Storcken, 2025. "Stability in Many-to-One Matching with Couples having Responsive Preferences," Papers 2507.07501, arXiv.org.
    • Handle: RePEc:arx:papers:2507.07501
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2507.07501
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    3. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    4. Bettina Klaus & Flip Klijn, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 653.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    5. Klaus, Bettina & Klijn, Flip & Nakamura, Toshifumi, 2009. "Corrigendum to "Stable matchings and preferences of couples" [J. Econ. Theory 121 (1) (2005) 75-106]," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2227-2233, September.
    6. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    7. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    8. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    9. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    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. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    2. 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.
    3. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    4. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.
    5. Shashwat Khare & Souvik Roy, 2025. "Characterizing Stability in Many-to-One Matching with Non-Responsive Couples," Papers 2507.07490, arXiv.org.
    6. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    7. 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.
    8. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
    9. Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    10. Dimitrov, Dinko & Lazarova, Emiliya A., 2008. "Coalitional Matchings," Coalition Theory Network Working Papers 37523, Fondazione Eni Enrico Mattei (FEEM).
    11. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    12. Thanh Nguyen & Rakesh Vohra, 2014. "Near Feasible Stable Matchings with Complementarities," PIER Working Paper Archive 14-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Tello, Benjamín, 2023. "Restricted complementarity and paths to stability in matching with couples," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 60-67.
    14. 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.
    15. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    16. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
    17. Bettina Klaus & Flip Klijn, 2007. "Fair and efficient student placement with couples," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 177-207, October.
    18. Itai Ashlagi & Mark Braverman & Avinatan Hassidim, 2014. "Stability in Large Matching Markets with Complementarities," Operations Research, INFORMS, vol. 62(4), pages 713-732, August.
    19. Chao Huang, 2025. "Matching to two sides," Papers 2509.10942, arXiv.org.
    20. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.

    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:2507.07501. 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: http://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.