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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.

Suggested Citation

  • Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-28, December.
  • Handle: RePEc:bpj:bejtec:v:contributions.6:y:2006:i:1:n:8
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    Cited by:

    1. Kohei Kawamura & József Sákovics, 2014. "Spillovers of Equal Treatment in Wage Offers," Scottish Journal of Political Economy, Scottish Economic Society, pages 487-501.
    2. Legros, Patrick & Newman, Andrew, 2010. "Co-ranking mates: Assortative matching in marriage markets," Economics Letters, Elsevier, vol. 106(3), pages 177-179, March.
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    4. Patrick Legros & Andrew F. Newman, 2007. "Beauty Is a Beast, Frog Is a Prince: Assortative Matching with Nontransferabilities," Econometrica, Econometric Society, pages 1073-1102.
    5. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, pages 1507-1534.
    6. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2017. "Optimal Tax Progressivity: An Analytical Framework," The Quarterly Journal of Economics, Oxford University Press, pages 1693-1754.
    7. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    8. Bilancini, Ennio & Boncinelli, Leonardo, 2013. "Disclosure of information in matching markets with non-transferable utility," Games and Economic Behavior, Elsevier, pages 143-156.
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    10. 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.
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    14. Wang, X. & Agatz, N.A.H. & Erera, A., 2015. "Stable Matching for Dynamic Ride-sharing Systems," ERIM Report Series Research in Management ERS-2015-006-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    15. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, pages 1939-1978.
    16. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    17. 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 - Economics Institute, Prague.
    18. Flanders, Sam, 2013. "Continuous Matching with Single Peaked Preferences," MPRA Paper 53668, University Library of Munich, Germany.
    19. Bilancini, Ennio & Boncinelli, Leonardo, 2014. "Instrumental cardinal concerns for social status in two-sided matching with non-transferable utility," European Economic Review, Elsevier, vol. 67(C), pages 174-189.
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