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Absolutely stable roommate problems

Author

Listed:
  • MAULEON, Ana

    (CEREC, Facultés universitaires Saint-Louis, B-1000 Brussels, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • MOLIS, Elena

    (Universidad de Granada, E-18011 Granada, Spain)

  • VANNETELBOSCH, Vincent

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • VERGOTE, Wouter

    (CEREC, Facultés universitaires Saint-Louis, B-1000 Brussels, Belgium; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

Abstract

Different solution concepts (core, stable sets, largest consistent set, ...) can be defined using either a direct or an indirect dominance relation. Direct dominance implies indirect dominance, but not the reverse. Hence, the predicted outcomes when assuming myopic (direct) or farsighted (indirect) agents could be very different. In this paper, we characterize absolutely stable roommate problems when preferences are strict. That is, we obtain the conditions on preference profiles such that indirect dominance implies direct dominance in roommate problems. Furthermore, we characterize absolutely stable roommate problems having a non-empty core. Finally, we show that, if the core of an absolutely stable roommate problem is not empty, it contains a unique matching in which all agents who mutually top rank each other are matched to one another and all other agents remain unmatched.

Suggested Citation

  • MAULEON, Ana & MOLIS, Elena & VANNETELBOSCH, Vincent & VERGOTE, Wouter, 2011. "Absolutely stable roommate problems," LIDAM Discussion Papers CORE 2011029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2011029
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    References listed on IDEAS

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    More about this item

    Keywords

    roommate problems; direct dominance; indirect dominance;
    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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