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The Uniqueness of Stable Matchings

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Author Info
Simon Clark (University of Edinburgh)

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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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Publisher Info
Article provided by Berkeley Electronic Press in its journal Contributions to Theoretical Economics.

Volume (Year): 6 (2006)
Issue (Month): 1 ()
Pages: 1283-1283
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Handle: RePEc:bep:thecon:v:6:y:2006:i:1:p:1283-1283

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Related research
Keywords: uniqueness matching marriage no crossing condition supermodularity Spence-Mirrlees single crossing condition

Find related papers by JEL classification:
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Simon Clark & Ravi Kanbur, 2004. "Stable Partnerships, Matching, and Local Public Goods," ESE Discussion Papers 82, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  2. Alcalde, J., 1995. "Exchange-Proofness or Divorce Proofness? Stability in a one Sided Matching Market," Papers 95-04, Valencia - Instituto de Investigaciones Economicas.
  3. Ted Bergstrom & David Lam, 1989. "The effects of cohort size on marriage markets in twentieth century Sweden," University of California at Santa Barbara, Economics Working Paper Series 1989, Department of Economics, UC Santa Barbara. [Downloadable!]
    Other versions:
  4. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August. [Downloadable!] (restricted)
  5. Legros, Patrick & Newman, Andrew F, 2002. "Monotone Matching in Perfect and Imperfect Worlds," Review of Economic Studies, Blackwell Publishing, vol. 69(4), pages 925-42, October.
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  6. John Ermisch & Marco Francesconi & Thomas Siedler, 2006. "Intergenerational Mobility and Marital Sorting," Economic Journal, Royal Economic Society, vol. 116(513), pages 659-679, 07. [Downloadable!] (restricted)
  7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January. [Downloadable!] (restricted)
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  8. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October. [Downloadable!] (restricted)
  9. Ted Bergstrom & David Lam, 1989. "The Two-Sex Problem and the Marriage Squeeze in an Equilibrium Model of Marriage Markets," University of California at Santa Barbara, Economics Working Paper Series 1989C, Department of Economics, UC Santa Barbara. [Downloadable!]
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!] (restricted)
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