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Stability against Robust Deviations in the Roommate Problem

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  • Hirata, Daisuke
  • 平田, 大祐
  • Kasuya, Yusuke
  • 糟谷, 祐介
  • Tomoeda, Kentaro
  • 友枝, 健太郎

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 no deviation from it is robust up to depth k. As a smaller k imposes a stronger requirement for a matching to be SaRD, we investigate the existence of a matching that is SaRD with a minimal depth k. We constructively demonstrate that a SaRD matching always exists for k=3 and establish sufficient conditions for k=1 and 2.
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Suggested Citation

  • Hirata, Daisuke & 平田, 大祐 & Kasuya, Yusuke & 糟谷, 祐介 & Tomoeda, Kentaro & 友枝, 健太郎, 2020. "Stability against Robust Deviations in the Roommate Problem," Discussion Papers 2020-02, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2020-02
    Note: This Version: March 11, 2020
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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. 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.
    5. Troyan, Peter & Delacrétaz, David & Kloosterman, Andrew, 2020. "Essentially stable matchings," Games and Economic Behavior, Elsevier, vol. 120(C), pages 370-390.

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    More about this item

    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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