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Impossibilities for roommate problems

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  • Özkal-Sanver, Ipek

Abstract

We establish three impossibility results for roommate problems. First, no single valued solution is Pareto optimal and anonymous. Next, no solution satisfies Pareto optimality, anonymity and converse consistency. Finally, no pseudo-refinement of the core satisfies consistency.

Suggested Citation

  • Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:360-363
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    References listed on IDEAS

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    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, 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. 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.
    5. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 373-397.
    6. 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.
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    Citations

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    Cited by:

    1. İpek Özkal-Sanver, 2013. "Minimal conversely consistent extension of the men-optimal solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(1), pages 89-99, January.
    2. Paula Jaramillo, 2017. "Minimal consistent enlargements of the immediate acceptance rule and the top trading cycles rule in school choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 177-195, January.
    3. repec:eee:gamebe:v:104:y:2017:i:c:p:43-58 is not listed on IDEAS
    4. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2017. "Cost of transformation: a measure on matchings," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Péter Biró & Elena Inarra & Elena Molis, 2014. "A new solution for the roommate problem: The Q-stable matchings," IEHAS Discussion Papers 1422, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    6. 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.
    7. Klaus, Bettina, 2017. "Consistency and its converse for roommate markets," Games and Economic Behavior, Elsevier, vol. 104(C), pages 43-58.
    8. 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.
    9. 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.

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