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Consistent enlargements of the core in roommate problems

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  • Duygu Nizamogullari
  • İpek Özkal-Sanver

Abstract

In this paper, we study consistent enlargement of a solution. By computing it, one actually evaluates the extent to which the solution would have to be expanded in order to be well-defined and consistent. We show that the union of stable matchings and the matching recommended by a single-valued, well-defined, individually rational, and consistent solution is a minimal consistent enlargement of the core. Although individual rationality is sufficient it is not a necessity. Next, we show that for any fixed order on the set of agents in the society, the union of stable matchings and the serial dictatorship matching is a minimal consistent enlargement of the core. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:kap:theord:v:79:y:2015:i:2:p:217-225
    DOI: 10.1007/s11238-014-9470-z
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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.
    2. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    3. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 461-471, March.
    4. Nizamogullari, Duygu & Özkal-Sanver, İpek, 2014. "Characterization of the core in full domain marriage problems," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 34-42.
    5. Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, vol. 81(C), pages 165-178.
    6. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
    7. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 373-397.
    8. Manabu Toda, 2006. "Monotonicity and Consistency in Matching Markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 13-31, April.
    9. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 647-667, October.
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    Cited by:

    1. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2018. "On societies choosing social outcomes, and their memberships: internal stability and consistency," Theory and Decision, Springer, vol. 84(1), pages 83-97, January.

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    More about this item

    Keywords

    Roommate problems; Core; Consistency; C78;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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