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Paths to Stability for Matching Markets with Couples

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Author Info
Bettina Klaus ()
Flip Klijn

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Abstract

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from `satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's (1990) result on path convergence to stability for decentralized singles markets. Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from `satisfying' blocking coalitions that yields a stable matching.

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Publisher Info
Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 604.04.

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Length: 17
Date of creation: 08 Feb 2004
Date of revision: 01 Dec 2005
Handle: RePEc:aub:autbar:604.04

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Related research
Keywords: Matching; Couples; Stability; Random Paths; Responsiveness.;

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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
D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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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. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July. [Downloadable!] (restricted)
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  3. 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)
  4. Bettina Klaus & Flip Klijn, 2002. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," UFAE and IAE Working Papers 552.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Oct 2005. [Downloadable!]
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  5. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July. [Downloadable!] (restricted)
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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. Claus-Jochen Haake & Bettina Klaus, 2008. "Stability and Nash implementation in matching markets with couples," Working Papers 399, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
    Other versions:
  2. Bettina Klaus & Flip Klijn, 2004. "Fair and Efficient Student Placement with Couples," UFAE and IAE Working Papers 616.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Mar 2006. [Downloadable!]
    Other versions:
  3. James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, Economics Bulletin, vol. 3(67), pages 1-12. [Downloadable!]
    Other versions:
  4. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer, vol. 36(3), pages 473-488, March. [Downloadable!] (restricted)
    Other versions:
  5. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
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