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A new solution for the roommate problem: The Q-stable matchings

Author

Listed:
  • Péter Biró

    (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences and Department of Economics, Stanford University)

  • Elena Inarra

    (BRiDGE, University of the Basque Country (UPV/EHU) and Instituto de Economía Pública)

  • Elena Molis

    (GLOBE, Departamento de Teoría e Historia Económica, Universidad de Granada)

Abstract

The aim of this paper is to propose a new solution for the roommate problem with strict references. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable matchings (Tan [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an efficient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.

Suggested Citation

  • Péter Biró & Elena Inarra & Elena Molis, 2014. "A new solution for the roommate problem: The Q-stable matchings," CERS-IE WORKING PAPERS 1422, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1422
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    References listed on IDEAS

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    1. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
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    Cited by:

    1. 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.
    2. Arnaud Zlatko Dragicevic, 2022. "Exchange Networks with Stochastic Matching," Games, MDPI, vol. 14(1), pages 1-18, December.

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    More about this item

    Keywords

    roommate problem; almost stable; maximum stable; absorbing set;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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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