AbstractIn 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Economics Letters.
Volume (Year): 118 (2013)
Issue (Month): 2 ()
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Acyclicity; Cycle; Kidney; Representation; Roommates; Symmetry;
Find related papers by JEL classification:
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
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- Alvaro Rodrigues-Neto, Jose, 2007.
"Representing roommates' preferences with symmetric utilities,"
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NBER Working Papers
10002, National Bureau of Economic Research, Inc.
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"Pairwise kidney exchange,"
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- Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2004. "Pairwise Kidney Exchange," NBER Working Papers 10698, National Bureau of Economic Research, Inc.
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- Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007.
"Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences,"
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- Ãœnver, M. Utku & SÃ¶nmez, Tayfun & Roth, Alvin, 2007. "Efficient Kidney Exchange: Coincidence of Wants in a Markets with Compatibility-Based Preferences," Scholarly Articles 2562809, Harvard University Department of Economics.
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