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Stability against Robust Deviations in the Roommate Problem

Author

Listed:
  • Daisuke Hirata

    (Hitotsubashi University)

  • Yusuke Kasuya

    (Kobe University)

  • Kentaro Tomoeda

    (University of Technology Sydney)

Abstract

We propose a new solution concept in the roommate problem, based on the �robustness� of deviations (i.e., blocking coalitions). We call a deviation from a matching robust up to depth k, if none of the deviators gets worse off than at the original matching after any sequence of at most k subsequent deviations. We say that a matching is stable against robust deviations (for short, SaRD) up to depth k, if there is no robust deviation up to depth k. As a smaller k imposes a stronger requirement for amatching to be SaRD, we investigate the existence of a matching that is SaRD with a minimal depth k. We constructively demonstrate that a SaRDmatching always exists for k = 3, and establish sufficient conditions for k = 1 and 2.

Suggested Citation

  • Daisuke Hirata & Yusuke Kasuya & Kentaro Tomoeda, 2019. "Stability against Robust Deviations in the Roommate Problem," Working Paper Series 2019/07, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    • Handle: RePEc:uts:ecowps:2019/07
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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. 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.
    3. G.-Herman Demeze-Jouatsa & Dominik Karos, 2023. "Farsighted Rationality in Hedonic Games," Dynamic Games and Applications, Springer, vol. 13(2), pages 462-479, June.
    4. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.
    5. 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).

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    More about this item

    Keywords

    matching; stability; robustness; roommate problem;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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