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Paths to Stability for Matching Markets with Couples

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  • Bettina Klaus

    ()

  • Flip Klijn

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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Bibliographic 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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Keywords: Matching; Couples; Stability; Random Paths; Responsiveness.;

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References

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  1. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
  2. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 708.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  3. Bettina Klaus & Flip Klijn & Jordi Massó, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Review of Economic Design, Springer, vol. 11(3), pages 175-184, November.
  4. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  5. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
  6. Jinpeng Ma, 1996. "On randomized matching mechanisms (*)," Economic Theory, Springer, vol. 8(2), pages 377-381.
  7. Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002. "Random paths to stability in the roommate problem," Discussion Papers 0102-65, Columbia University, Department of Economics.
  8. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
  9. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  10. 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.
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Citations

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Cited by:
  1. Bo Chen & Satoru Fujishige & Zaifu Yang, 2010. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," KIER Working Papers 749, Kyoto University, Institute of Economic Research.
  2. Bettina Klaus & Flip Klijn, 2004. "Fair and Efficient Student Placement with Couples," Working Papers 145, Barcelona Graduate School of Economics.
  3. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1340008-1-1.
  4. James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-12.
  5. Yang, Yi-You, 2012. "On the accessibility of core-extensions," Games and Economic Behavior, Elsevier, vol. 74(2), pages 687-698.
  6. Bettina Klaus & Flip Klijn & Markus Walzl, 2009. "Farsighted Stability for Roommate Markets," Working Papers 385, Barcelona Graduate School of Economics.
  7. Utku Unver & Hideo Konishi, 2005. "Credible Group Stability in Multi-Partner Matching Problems," 2005 Meeting Papers 208, Society for Economic Dynamics.
  8. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.
  9. 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.
  10. Vilmos Komornik & Christelle Viauroux, 2012. "Conditional Stable Matchings," UMBC Economics Department Working Papers 12-03, UMBC Department of Economics.
  11. Alfredo Salgado-Torres, 2012. "A simple decentralized matching mechanism in markets with couples," Economics Bulletin, AccessEcon, vol. 32(3), pages 2044-2055.
  12. repec:ebl:ecbull:v:3:y:2008:i:67:p:1-12 is not listed on IDEAS
  13. Bettina Klaus & Frédéric Payot, 2013. "Paths to Stability in the Assignment Problem," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 13.14, Université de Lausanne, Faculté des HEC, DEEP.

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