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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.

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Bibliographic Info

Article provided by Elsevier in its journal Economics Letters.

Volume (Year): 118 (2013)
Issue (Month): 2 ()
Pages: 304-306

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Handle: RePEc:eee:ecolet:v:118:y:2013:i:2:p:304-306

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Web page: http://www.elsevier.com/locate/ecolet

Related research

Keywords: Acyclicity; Cycle; Kidney; Representation; Roommates; Symmetry;

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  1. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," NBER Working Papers 10002, National Bureau of Economic Research, Inc.
  2. 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.
  3. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Boston College Working Papers in Economics 620, Boston College Department of Economics.
  4. José Álvaro Rodrigues Neto, 2006. "Representing Roomates' Preferences with Symmetric Utilities," Working Papers Series 105, Central Bank of Brazil, Research Department.
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