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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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    Citations

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    Cited by:

    1. 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.
    2. Lauermann, Stephan & Nöldeke, Georg, 2014. "Stable marriages and search frictions," Journal of Economic Theory, Elsevier, vol. 151(C), pages 163-195.
    3. Sang-Chul Suh & Quan Wen, 2008. "Subgame perfect implementation of stable matchings in marriage problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 163-174, June.
    4. 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.
    5. Flanders, Sam, 2014. "Matching Markets with N-Dimensional Preferences," MPRA Paper 53669, University Library of Munich, Germany.
    6. Legros, Patrick & Newman, Andrew, 2010. "Co-ranking mates: Assortative matching in marriage markets," Economics Letters, Elsevier, vol. 106(3), pages 177-179, March.
    7. Patrick Legros & Andrew F. Newman, 2007. "Beauty Is a Beast, Frog Is a Prince: Assortative Matching with Nontransferabilities," Econometrica, Econometric Society, vol. 75(4), pages 1073-1102, July.
    8. Flanders, Sam, 2013. "Continuous Matching with Single Peaked Preferences," MPRA Paper 53668, University Library of Munich, Germany.
    9. Alkan, Ahmet & Anbarci, Nejat & Sarpça, Sinan, 2012. "An exploration in school formation: Income vs. Ability," Economics Letters, Elsevier, vol. 117(2), pages 500-504.
    10. Kohei Kawamura & József Sákovics, 2014. "Spillovers of Equal Treatment in Wage Offers," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(5), pages 487-501, November.
    11. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    12. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    13. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    14. Klumpp, Tilman, 2009. "Two-sided matching with spatially differentiated agents," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 376-390, May.
    15. Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.
    16. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2014. "Household consumption when marriage is stable," IFS Working Papers W14/26, Institute for Fiscal Studies.
    17. 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.
    18. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    19. 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.
    20. 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.
    21. 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.
    22. Holzman, Ron & Samet, Dov, 2014. "Matching of like rank and the size of the core in the marriage problem," Games and Economic Behavior, Elsevier, vol. 88(C), pages 277-285.
    23. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0543-9 is not listed on IDEAS
    24. repec:eee:matsoc:v:91:y:2018:i:c:p:42-50 is not listed on IDEAS
    25. 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.

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