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A note on roommate problems with a limited number of rooms

Author

Listed:
  • Duygu Nizamogullari

    (Piri Reis University)

  • İpek Özkal-Sanver

    (İstanbul Bilgi University)

Abstract

Classical roommate problems define individual rationality by conceiving remaining single as the “outside option”. This conception implicitly assumes that there are always some empty rooms to be shared. However, there are many instances when this is not the case. We introduce roommate problems with a limited number of rooms, where the “outside option” is “having no room”. In this general framework, we show that the core equals the set of Pareto optimal and stable matchings.

Suggested Citation

  • Duygu Nizamogullari & İpek Özkal-Sanver, 2022. "A note on roommate problems with a limited number of rooms," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 553-560, December.
    • Handle: RePEc:spr:reecde:v:26:y:2022:i:4:d:10.1007_s10058-022-00297-4
    DOI: 10.1007/s10058-022-00297-4
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    References listed on IDEAS

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    1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    2. Klaus, Bettina, 2017. "Consistency and its converse for roommate markets," Games and Economic Behavior, Elsevier, vol. 104(C), pages 43-58.
    3. Burak Can & Bettina Klaus, 2013. "Consistency and population sensitivity properties in marriage and roommate markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 835-862, October.
    4. Klaus, Bettina, 2011. "Competition and resource sensitivity in marriage and roommate markets," Games and Economic Behavior, Elsevier, vol. 72(1), pages 172-186, May.
    5. Wouter Vergote, 2019. "Revisiting stability in one-to-one matching problems," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 59-75, May.
    6. Morrill, Thayer, 2010. "The roommates problem revisited," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1739-1756, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Individual rationality; Pareto optimality; Core;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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