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The Uniqueness of Stable Matchings

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  • Clark Simon

    ()
    (University of Edinburgh)

Abstract

This paper analyses conditions on agents' preferences for a unique stable matching in models of two-sided matching with non-transferable utility. The No Crossing Condition (NCC) is sufficient for uniqueness; it is based on the notion that a person's characteristics, for example their personal qualities or their productive capabilities, not only form the basis of their own attraction to the opposite sex but also determine their own preferences. The paper also shows that a weaker condition, alpha-reducibility, is both necessary and sufficient for a population and any of its subpopulations to have a unique stable matching. If preferences are based on utility functions with agents' characteristics as arguments, then the NCC may be easy to verify. The paper explores conditions on utility functions which imply that the NCC is satisfied whatever the distribution of characteristics. The usefulness of this approach is illustrated by two simple models of household formation.

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Bibliographic Info

Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 6 (2006)
Issue (Month): 1 (December)
Pages: 1-28

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Handle: RePEc:bpj:bejtec:v:contributions.6:y:2006:i:1:n:8

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Cited by:
  1. Bilancini, Ennio & Boncinelli, Leonardo, 2013. "Disclosure of information in matching markets with non-transferable utility," Games and Economic Behavior, Elsevier, vol. 82(C), pages 143-156.
  2. Patrick Legros & Andrew Newman, 2007. "Beauty is a beast, frog is a prince: assortative matching in a nontransferable world," ULB Institutional Repository 2013/7022, ULB -- Universite Libre de Bruxelles.
  3. Alkan, Ahmet & Anbarci, Nejat & Sarpça, Sinan, 2012. "An exploration in school formation: Income vs. Ability," Economics Letters, Elsevier, vol. 117(2), pages 500-504.
  4. Sang-Chul Suh & Quan Wen, 2006. "The Eeckhout Condition and the Subgame Perfect Implementation of Stable Matching," 2006 Meeting Papers 176, Society for Economic Dynamics.
  5. Ennio Bilancini & Leonardo Boncinelli, 2014. "Instrumental Cardinal Concerns for Social Status in Two-Sided Matching with Non-Transferable Utility," Center for Economic Research (RECent) 095, University of Modena and Reggio E., Dept. of Economics.
  6. Mario Vozar, 2010. "The Effect of Time in a Multi-Dimensional Marriage Market Model," CERGE-EI Working Papers wp417, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  7. Kohei, Kawamura & József, Sákovics, 2013. "Spillovers of Equal Treatment in Wage Offers," SIRE Discussion Papers 2013-15, Scottish Institute for Research in Economics (SIRE).
  8. Klumpp, Tilman, 2009. "Two-sided matching with spatially differentiated agents," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 376-390, May.
  9. Flanders, Sam, 2014. "Matching Markets with N-Dimensional Preferences," MPRA Paper 53669, University Library of Munich, Germany.
  10. Sang-Chul Suh & Quan Wen, 2008. "Subgame perfect implementation of stable matchings in marriage problems," Social Choice and Welfare, Springer, vol. 31(1), pages 163-174, June.
  11. Nikhil Agarwal & William Diamond, 2013. "Identification and Estimation in Two-Sided Matching Markets," Cowles Foundation Discussion Papers 1905, Cowles Foundation for Research in Economics, Yale University, revised Feb 2014.
  12. Flanders, Sam, 2013. "Continuous Matching with Single Peaked Preferences," MPRA Paper 53668, University Library of Munich, Germany.
  13. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.
  14. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.

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