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Acyclic roommates

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  • Rodrigues-Neto, José Alvaro

Abstract

In the context of the stable roommates problem, this paper provides an alternative characterization of acyclic instances with n roommates; one that requires checking n−1 fewer equations than symmetry of the utility functions (Rodrigues-Neto, 2007). We introduce the concepts of agent-cycles and cycle equations and prove that an instance is acyclic if and only if there exists a representation of preferences such that all cycle equations of agent-cycles of length 3 containing an agent i hold. In this case, there is a unique stable matching.

Suggested Citation

  • Rodrigues-Neto, José Alvaro, 2013. "Acyclic roommates," Economics Letters, Elsevier, vol. 118(2), pages 304-306.
  • Handle: RePEc:eee:ecolet:v:118:y:2013:i:2:p:304-306
    DOI: 10.1016/j.econlet.2012.11.027
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    References listed on IDEAS

    as
    1. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
    2. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    3. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, Oxford University Press, vol. 119(2), pages 457-488.
    4. Alvaro Rodrigues-Neto, Jose, 2007. "Representing roommates' preferences with symmetric utilities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 545-550, July.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Acyclicity; Cycle; Kidney; Representation; Roommates; Symmetry;

    JEL classification:

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

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