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Weak stability against robust deviations and the bargaining set in the roommate problem

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  • Hirata, Daisuke
  • Kasuya, Yusuke
  • Tomoeda, Kentaro

Abstract

We propose a new solution concept in the roommate problem, weak stability against robust deviations (wSaRD), by weakening a similar concept of Hirata et al. (2021). We identify a common sufficient condition for wSaRD and weak stability of Klijn and Massó (2003). We can always construct a weakly efficient matching satisfying this condition. Consequently, we can always find a wSaRD matching within the bargaining set. This is in contrast with the original, stronger concept of Hirata et al. (2021), which does not always intersect with the bargaining set.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:mateco:v:105:y:2023:i:c:s0304406823000113
    DOI: 10.1016/j.jmateco.2023.102818
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    References listed on IDEAS

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    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
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    5. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
    6. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
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    9. Biró, Péter & Iñarra, Elena & Molis, Elena, 2016. "A new solution concept for the roommate problem: Q-stable matchings," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 74-82.
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    Cited by:

    1. 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.
    2. Herings, P.J.J. & Zhou, Yu, 2025. "Harmonious Equilibria in Roommate Problems," Discussion Paper 2025-001, Tilburg University, Center for Economic Research.

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