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Absorbing sets in roommate problems

Author

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  • Iñarra, E.
  • Larrea, C.
  • Molis, E.

Abstract

We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of agents with no incentive to change partners. These “satisfied” agents are paired in the same stable manner. In the case of multiple absorbing sets we find that any two such sets differ only in how satisfied agents are matched with each other.

Suggested Citation

  • Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, vol. 81(C), pages 165-178.
    • Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:165-178
    DOI: 10.1016/j.geb.2013.04.008
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    References listed on IDEAS

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    Citations

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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. Korpela, Ville & Lombardi, Michele & Saulle, Riccardo D., 2024. "Designing rotation programs: Limits and possibilities," Games and Economic Behavior, Elsevier, vol. 143(C), pages 77-102.
    3. Wouter Vergote, 2019. "Revisiting stability in one-to-one matching problems," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 59-75, May.
    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. Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.
    6. José Luis Contreras & Juan Pablo Torres-Martínez, 2021. "The roommate problem with externalities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 149-165, March.
    7. Ana Mauleon & Elena Molis & Vincent Vannetelbosch & Wouter Vergote, 2014. "Dominance invariant one-to-one matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 925-943, November.
    8. Nax, Heinrich H. & Pradelski, Bary S. R., 2015. "Evolutionary dynamics and equitable core selection in assignment games," LSE Research Online Documents on Economics 65428, London School of Economics and Political Science, LSE Library.
    9. 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).
    10. 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..
    11. 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.
    12. Agustin G. Bonifacio & Elena Inarra & Pablo Neme, 2020. "A characterization of absorbing sets in coalition formation games," Papers 2009.11689, arXiv.org, revised May 2024.
    13. Duygu Nizamogullari & İpek Özkal-Sanver, 2015. "Consistent enlargements of the core in roommate problems," Theory and Decision, Springer, vol. 79(2), pages 217-225, September.
    14. Agustín G. Bonifacio & Elena Inarra & Pablo Neme, 2022. "Stable Decompositions of Coalition Formation Games," Working Papers 110, Red Nacional de Investigadores en Economía (RedNIE).

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    More about this item

    Keywords

    Roommate problem; Stability; Absorbing sets;
    All these keywords.

    JEL classification:

    • 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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