IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2503.24010.html
   My bibliography  Save this paper

Roommates with Convex Preferences

Author

Listed:
  • Sophie Bade

Abstract

Roommate problems with convex preferences always have stable matchings. Efficiency and individual rationality are, moreover, compatible with strategyproofness in such convex roommate problems. Both of these results fail without the assumption of convexity. In the environment under study, preferences are convex if and only if they are single peaked. Any individually rational and convex roommate problem is homomorphic to a marriage market where an agent's gender corresponds to the direction of the agent's top-ranked partner. The existence of stable matchings then follows from the existence of stable matchings in marriage markets. To prove the second existence result, I define an efficient, individually rational, and strategyproof mechanism for convex roommate problems. To calculate outcomes, this mechanism starts with all agents being single and then gradually reassigns agents to better partners by performing minimal Pareto improvements. Whenever it becomes clear that some agent cannot be part of any further Pareto improvement, such an agent is matched.

Suggested Citation

  • Sophie Bade, 2025. "Roommates with Convex Preferences," Papers 2503.24010, arXiv.org.
    • Handle: RePEc:arx:papers:2503.24010
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2503.24010
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuki Tamura, 2022. "Object reallocation problems under single-peaked preferences: two characterizations of the crawler," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 537-565, 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. Sumit Goel & Yuki Tamura, 2025. "TTC Domains," Papers 2501.15422, arXiv.org, revised Apr 2025.
    2. Tamura, Yuki & Hosseini, Hadi, 2022. "The crawler: Three equivalence results for object (re)allocation problems when preferences are single-peaked," Journal of Economic Theory, Elsevier, vol. 203(C).

    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:2503.24010. 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.