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Stability and Nash implementation in matching markets with couples

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Author Info
Claus-Jochen Haake () (Institute of Mathematical Economics, Bielefeld University)
Bettina Klaus () (Baker Library, Harvard Business School)

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Abstract

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-399.pdf
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File Function: First version, 2008
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Publisher Info
Paper provided by Bielefeld University, Institute of Mathematical Economics in its series Working Papers with number 399.

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Length: 17 pages
Date of creation: Aug 2008
Date of revision:
Handle: RePEc:bie:wpaper:399

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Web page: http://www.imw.uni-bielefeld.de/
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Related research
Keywords: matching with couples; (Maskin) monotonicity; Nash implementation; stability; weakly responsive preferences;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation
J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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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. Haake,Claus-Jochen & Klaus,Bettina, 2005. "Monotonicity and Nash Implementation in Matching Markets with Contracts," Research Memoranda 028, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
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  2. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February. [Downloadable!] (restricted)
  3. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
  4. Klaus, Bettina & Klijn, Flip & Nakamura, Toshifumi, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," Research Memoranda 025, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  5. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October. [Downloadable!] (restricted)
  6. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March. [Downloadable!] (restricted)
  7. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708. [Downloadable!] (restricted)
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  8. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November. [Downloadable!] (restricted)
  9. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September. [Downloadable!]
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  10. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January. [Downloadable!] (restricted)
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