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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 Barcelona Graduate School of Economics in its series Working Papers with number 156.

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Date of creation: Oct 2004
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Handle: RePEc:bge:wpaper:156

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Related research

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

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References

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  1. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  3. 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.
  4. Ma, Jinpeng, 1996. "On Randomized Matching Mechanisms," Economic Theory, Springer, vol. 8(2), pages 377-81, August.
  5. Bettina Klaus & Flip Klijn, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," UFAE and IAE Working Papers 653.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. 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.
  7. Klaus, Bettina & Klijn, Flip & Massó, Jordi, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20024, Maastricht University.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
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Citations

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Cited by:
  1. Claus-Jochen Haake & Bettina-Elisabeth Klaus, 2008. "Stability and Nash Implementation in Matching Markets with Couples," Harvard Business School Working Papers 09-017, Harvard Business School.
  2. 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.
  3. James Boudreau, 2008. "Preference Structure and Random Paths to Stability in Matching Markets," Economics Bulletin, AccessEcon, vol. 3(67), pages 1-12.
  4. Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Hungarian Academy of Sciences.
  5. Klaus, Bettina & Klijn, Flip, 2007. "Fair and efficient student placement with couples," Open Access publications from Maastricht University urn:nbn:nl:ui:27-20025, Maastricht University.
  6. Hideo Konishi & M. Utku Ünver, 2003. "Credible Group Stability in Multi-Partner Matching Problems," Working Papers 2003.115, Fondazione Eni Enrico Mattei.
  7. M.Utku Unver & Fuhito Kojima, 2006. "Random Paths to Pairwise Stability in Many-to-Many Matching Problems: A Study on Market Equilibration," Working Papers 256, University of Pittsburgh, Department of Economics, revised Jan 2006.
  8. Alfredo Salgado-Torres, 2012. "A simple decentralized matching mechanism in markets with couples," Economics Bulletin, AccessEcon, vol. 32(3), pages 2044-2055.
  9. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.
  10. repec:ebl:ecbull:v:3:y:2008:i:67:p:1-12 is not listed on IDEAS

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