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Monotonicity and Nash Implementation in Matching Markets with Contracts

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  • Haake,Claus-Jochen
  • Klaus,Bettina

    (METEOR)

Abstract

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theore m 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.

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Bibliographic Info

Paper provided by Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 028.

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Date of creation: 2005
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Handle: RePEc:unm:umamet:2005028

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Postal: P.O. Box 616, 6200 MD Maastricht
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Web page: http://www.maastrichtuniversity.nl/
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Keywords: microeconomics ;

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  1. 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.
  2. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
  3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  4. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708.
  5. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
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  7. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33.
  8. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
  9. Sonmez, Tayfun, 1996. "Implementation in generalized matching problems," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 429-439.
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  17. John W. Hatfield & Paul Milgrom, 2005. "Auctions, Matching and the Law of Aggregate Demand," Levine's Bibliography 122247000000000780, UCLA Department of Economics.
  18. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-40, June.
  19. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
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Cited by:
  1. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer, vol. 53(3), pages 561-589, August.
  2. Toyotaka Sakai, 2011. "A note on strategy-proofness from the doctor side in matching with contracts," Review of Economic Design, Springer, vol. 15(4), pages 337-342, December.

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