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

Author

Listed:
  • Peter Biro

    (Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences.)

  • Elena Iñarra

    (University of the Basque Country (UPV/EHU) and Instituto de Economia Publica.)

  • Elena Molis

    (Department of Economic Theory and Economic History, University of Granada.)

Abstract

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable matchings (Tan [30] [32]). We nd 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 o er an ecient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set

Suggested Citation

  • Peter Biro & Elena Iñarra & Elena Molis, 2014. "A new solution for the roommate problem. The Q-stable matchings," ThE Papers 14/04, Department of Economic Theory and Economic History of the University of Granada..
    • Handle: RePEc:gra:wpaper:14/04
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    References listed on IDEAS

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    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

    Cost allocation;

    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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