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A bargaining set for roommate problems

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  • Atay, Ata
  • Mauleon, Ana
  • Vannetelbosch, Vincent

Abstract

Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.

Suggested Citation

  • Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    • Handle: RePEc:eee:mateco:v:94:y:2021:i:c:s0304406820301427
    DOI: 10.1016/j.jmateco.2020.102465
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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. G.-Herman Demeze-Jouatsa & Dominik Karos, 2023. "Farsighted Rationality in Hedonic Games," Dynamic Games and Applications, Springer, vol. 13(2), pages 462-479, June.
    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. 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.
    6. 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.

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    More about this item

    Keywords

    Roommate problem; Matching; (Weak) stability; Bargaining set;
    All these keywords.

    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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