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Stability and Nash implementation in matching markets with couples

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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.

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References

  • Alkan A., Gale D. (2003) Stable schedule matching under revealed preferences. Journal of Economic Theory 112: 289–306

    Article  Google Scholar 

  • Gale D., Shapley L. (1962) College admissions and the stability of marriage. American Mathematical Monthly 69: 9–15

    Article  Google Scholar 

  • 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.

  • Hatfield J.W., Milgrom P. (2005) Matching with contracts. American Economic Review 95(4): 913–935

    Article  Google Scholar 

  • Jackson M.O. (2001) A crash course in implementation theory. Social Choice and Welfare 18(3): 655–708

    Article  Google Scholar 

  • Kara T., Sönmez T. (1996) Nash implementation of matching rules. Journal of Economic Theory 68: 425–439

    Article  Google Scholar 

  • Kara T., Sönmez T. (1997) Implementation of college admission rules. Economic Theory 9: 197–218

    Google Scholar 

  • Kelso A.S., Crawford V.P. (1982) Job matching, coalition formation, and gross substitutes. Econometrica 6: 1483–1504

    Article  Google Scholar 

  • Klaus B., Klijn F. (2005) Stable matchings and preferences of couples. Journal of Economic Theory 121: 75–106

    Article  Google Scholar 

  • Klaus B., Klijn F. (2007) Paths to stability for matching markets with couples. Games and Economic Behavior 58: 154–171

    Article  Google Scholar 

  • Klaus, B., Klijn, F., & Nakamura, T. (2008). Corrigendum: Stable matchings and preferences of couples. Journal of Economic Theory (Forthcoming)

  • Maskin, E. (1977). Nash equilibrium and welfare optimality. MIT working paper.

  • Maskin E. (1999) Nash equilibrium and welfare optimality. Review of Economic Studies 66: 23–38

    Article  Google Scholar 

  • Maskin, E., & Sjöström, T. (2002). Implementation theory. In Handbook of social choice and welfare (Vol. 1). Amsterdam: North-Holland.

  • Moore J., Repullo R. (1990) Nash implementation: A full characterization. Econometrica 58(5): 1083–1099

    Article  Google Scholar 

  • Ronn E. (1990) NP-complete stable matching problems. Journal of Algorithms 11: 285–304

    Article  Google Scholar 

  • 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: 991–1016

    Article  Google Scholar 

  • Roth A.E. (1984b) Stability and polarization of interests in job matching. Econometrica 52: 47–57

    Article  Google Scholar 

  • Roth A.E. (1985) The college admissions problem is not equivalent to the marriage problem. Journal of Economic Theory 36: 277–288

    Article  Google Scholar 

  • 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: 748–780

    Article  Google Scholar 

  • Roth A.E., Sotomayor M.A. (1990) Two-sided matching: A study in game-theoretic modeling and analysis. Econometric Society Monographs. Cambridge University Press, Cambridge

    Google Scholar 

  • Shapley L.S., Scarf H. (1974) On cores and indivisibility. Journal of Mathematical Economics 1: 23–28

    Article  Google Scholar 

  • Sönmez T. (1996) Implementation in generalized matching problems. Journal of Mathematical Economics 26: 429–439

    Article  Google Scholar 

  • Thomson W. (1996) Concepts of implementation. Japanese Economic Review 47: 133–143

    Article  Google Scholar 

  • Yamato T. (1992) On Nash implementation of social choice correspondences. Games and Economic Behavior 4: 484–492

    Article  Google Scholar 

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Correspondence to Bettina Klaus.

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Haake, CJ., Klaus, B. Stability and Nash implementation in matching markets with couples. Theory Decis 69, 537–554 (2010). https://doi.org/10.1007/s11238-008-9122-2

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  • DOI: https://doi.org/10.1007/s11238-008-9122-2

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