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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Web page: http://www.elsevier.com/locate/ecolet
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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- Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2004.
"Pairwise Kidney Exchange,"
122247000000000350, UCLA Department of Economics.
- Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Game Theory and Information 0408001, EconWPA, revised 16 Feb 2005.
- Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Boston College Working Papers in Economics 620, Boston College Department of Economics.
- Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2004. "Pairwise Kidney Exchange," NBER Working Papers 10698, National Bureau of Economic Research, Inc.
- Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003.
Game Theory and Information
- 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.
- 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.
- José Álvaro Rodrigues Neto, 2006.
"Representing Roomates' Preferences with Symmetric Utilities,"
Working Papers Series
105, Central Bank of Brazil, Research Department.
- Alvaro Rodrigues-Neto, Jose, 2007. "Representing roommates' preferences with symmetric utilities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 545-550, July.
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