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Theory and Decision

, Volume 69, Issue 4, pp 537–554 | Cite as

Stability and Nash implementation in matching markets with couples

  • Claus-Jochen Haake
  • Bettina Klaus
Article

Abstract

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (J Econ Theory 21: 75–106, 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.

Keywords

Matching with couples (Maskin) Monotonicity Nash implementation Stability Weakly responsive preferences 

JEL Classification

C62 C78 D78 J41 

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References

  1. Alkan A., Gale D. (2003) Stable schedule matching under revealed preferences. Journal of Economic Theory 112: 289–306CrossRefGoogle Scholar
  2. Gale D., Shapley L. (1962) College admissions and the stability of marriage. American Mathematical Monthly 69: 9–15CrossRefGoogle Scholar
  3. Haake, C.-J., & Klaus, B. (2008). Monotonicity and Nash implementation in matching markets with contracts. Economic Theory (in press). doi: 10.1007/s00199-008-0399-8.
  4. Hatfield J.W., Milgrom P. (2005) Matching with contracts. American Economic Review 95(4): 913–935CrossRefGoogle Scholar
  5. Jackson M.O. (2001) A crash course in implementation theory. Social Choice and Welfare 18(3): 655–708CrossRefGoogle Scholar
  6. Kara T., Sönmez T. (1996) Nash implementation of matching rules. Journal of Economic Theory 68: 425–439CrossRefGoogle Scholar
  7. Kara T., Sönmez T. (1997) Implementation of college admission rules. Economic Theory 9: 197–218Google Scholar
  8. Kelso A.S., Crawford V.P. (1982) Job matching, coalition formation, and gross substitutes. Econometrica 6: 1483–1504CrossRefGoogle Scholar
  9. Klaus B., Klijn F. (2005) Stable matchings and preferences of couples. Journal of Economic Theory 121: 75–106CrossRefGoogle Scholar
  10. Klaus B., Klijn F. (2007) Paths to stability for matching markets with couples. Games and Economic Behavior 58: 154–171CrossRefGoogle Scholar
  11. Klaus, B., Klijn, F., & Nakamura, T. (2008). Corrigendum: Stable matchings and preferences of couples. Journal of Economic Theory (Forthcoming)Google Scholar
  12. Maskin, E. (1977). Nash equilibrium and welfare optimality. MIT working paper.Google Scholar
  13. Maskin E. (1999) Nash equilibrium and welfare optimality. Review of Economic Studies 66: 23–38CrossRefGoogle Scholar
  14. Maskin, E., & Sjöström, T. (2002). Implementation theory. In Handbook of social choice and welfare (Vol. 1). Amsterdam: North-Holland.Google Scholar
  15. Moore J., Repullo R. (1990) Nash implementation: A full characterization. Econometrica 58(5): 1083–1099CrossRefGoogle Scholar
  16. Ronn E. (1990) NP-complete stable matching problems. Journal of Algorithms 11: 285–304CrossRefGoogle Scholar
  17. Roth A.E. (1984a) The evolution of the labor market for medical interns and residents: a case study in game theory. Journal of Political Economy 92: 991–1016CrossRefGoogle Scholar
  18. Roth A.E. (1984b) Stability and polarization of interests in job matching. Econometrica 52: 47–57CrossRefGoogle Scholar
  19. Roth A.E. (1985) The college admissions problem is not equivalent to the marriage problem. Journal of Economic Theory 36: 277–288CrossRefGoogle Scholar
  20. Roth A.E., Peranson E. (1999) The redesign of the matching market for American physicians: Some engineering aspects of economic design. American Economic Review 89: 748–780CrossRefGoogle Scholar
  21. Roth A.E., Sotomayor M.A. (1990) Two-sided matching: A study in game-theoretic modeling and analysis. Econometric Society Monographs. Cambridge University Press, CambridgeGoogle Scholar
  22. Shapley L.S., Scarf H. (1974) On cores and indivisibility. Journal of Mathematical Economics 1: 23–28CrossRefGoogle Scholar
  23. Sönmez T. (1996) Implementation in generalized matching problems. Journal of Mathematical Economics 26: 429–439CrossRefGoogle Scholar
  24. Thomson W. (1996) Concepts of implementation. Japanese Economic Review 47: 133–143CrossRefGoogle Scholar
  25. Yamato T. (1992) On Nash implementation of social choice correspondences. Games and Economic Behavior 4: 484–492CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2008

Authors and Affiliations

  1. 1.Institute of Mathematical EconomicsBielefeld UniversityBielefeldGermany
  2. 2.Harvard Business School, Baker LibraryBostonUSA

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