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A bargaining set for roommate problems

Author

Listed:
  • ATAY Ata,

    (Hungarian Academy of Sciences)

  • MAULEON Ana,

    (Université Saint-Louis, Bruxelles)

  • VANNETELBOSCH Vincent,

    (Université catholique de Louvain, CORE, Belgium)

Abstract

Since stable matchings may not exist, we adopt a weaker notion of stability for solving the roommate problem: The bargaining set. Klijn and Masso (2003) show that the bargaining set coincides with the set of weakly stable and weakly efficient matchings in the marriage problem. First, we show that a weakly stable matching always exists in the roommate problem. However, weak stability is not sufficient for a matching to be in the bargaining set. Second, we prove that the bargaining set is always non-empty. Finally, as Klijn and Masso (2003) get for the marriage problem, we show that the bargaining set coincides with the set of weakly stable and weakly efficient matchings in the roommate problem.

Suggested Citation

  • ATAY Ata, & MAULEON Ana, & VANNETELBOSCH Vincent,, 2019. "A bargaining set for roommate problems," LIDAM Discussion Papers CORE 2019012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2019012
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2019.html
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    Citations

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    Cited by:

    1. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    2. Piazza, Adriana & Torres-Martínez, Juan Pablo, 2024. "Coalitional stability in matching problems with externalities and random preferences," Games and Economic Behavior, Elsevier, vol. 143(C), pages 321-339.
    3. Hirata, Daisuke & Kasuya, Yusuke & Tomoeda, Kentaro, 2023. "Weak stability against robust deviations and the bargaining set in the roommate problem," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    4. Aditya Kuvalekar, 2022. "Matching with Incomplete Preferences," Papers 2212.02613, arXiv.org, revised Nov 2023.
    5. Herings, P.J.J. & Zhou, Yu, 2025. "Harmonious Equilibria in Roommate Problems," Other publications TiSEM bf3f5d8c-9cd0-4b5c-89f2-0, Tilburg University, School of Economics and Management.
    6. Hirata, Daisuke & Kasuya, Yusuke & Tomoeda, Kentaro, 2021. "Stability against robust deviations in the roommate problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 474-498.
    7. G.-Herman Demeze-Jouatsa & Dominik Karos, 2023. "Farsighted Rationality in Hedonic Games," Dynamic Games and Applications, Springer, vol. 13(2), pages 462-479, June.
    8. Pongou, Roland & Tondji, Jean-Baptiste, 2024. "The reciprocity set," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    9. Kondor, Gábor, 2022. "Egyoldali párosítási piacok nehézségi eredményei magasabb dimenzióban [Hardness results of one-sided matching markets in higher dimensions]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(7), pages 825-840.

    More about this item

    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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