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Monotonicity and Nash implementation in matching markets with contracts

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  • Claus-Jochen Haake

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Bettina Klaus

    ()
    (Department of Economics, Maastricht University)

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 (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-372.pdf
File Function: First version, 2005
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 372.

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Length: 21 pages
Date of creation: Aug 2005
Date of revision:
Handle: RePEc:bie:wpaper:372

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Keywords: matching with contracts; (Maskin) monotonicity; Nash implementation; stability.;

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References

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  1. Federico Echenique & Jorge Oviedo, 2003. "A Theory of Stability in Many-to-many Matching Markets," Levine's Working Paper Archive 666156000000000374, David K. Levine.
  2. John W. Hatfield & Paul Milgrom, 2005. "Auctions, Matching and the Law of Aggregate Demand," Levine's Bibliography 122247000000000780, UCLA Department of Economics.
  3. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers, Pennsylvania State University, Department of Economics 5-01-1, Pennsylvania State University, Department of Economics.
  4. 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, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  5. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 36(2), pages 277-288, August.
  6. Thomson, W., 1996. "Monotonic Extension on Economic Domains," RCER Working Papers 431, University of Rochester - Center for Economic Research (RCER).
  7. Paul Milgrom, 2003. "Matching with Contracts," Working Papers, Stanford University, Department of Economics 03003, Stanford University, Department of Economics.
  8. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 47-57, January.
  9. 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, American Economic Association, vol. 81(3), pages 415-40, June.
  10. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521437882.
  11. Sonmez, T., 1995. "Implementation in Generalized Matching Problems," Papers, Michigan - Center for Research on Economic & Social Theory 95-03, Michigan - Center for Research on Economic & Social Theory.
  12. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, Elsevier, vol. 112(2), pages 289-306, October.
  13. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  14. Ehlers, Lars, 2004. "Monotonic and implementable solutions in generalized matching problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 114(2), pages 358-369, February.
  15. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1083-99, September.
  16. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  17. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, Elsevier, vol. 68(2), pages 425-439, February.
  18. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, Springer, vol. 9(2), pages 197-218.
  19. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521536721.
  20. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, American Economic Association, vol. 84(4), pages 992-1044, September.
  21. Hurwicz, Leonid & Schmeidler, David, 1978. "Construction of Outcome Functions Guaranteeing Existence and Pareto Optimality of Nash Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 46(6), pages 1447-74, November.
  22. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, Elsevier, vol. 4(3), pages 484-492, July.
  23. 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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Citations

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Cited by:
  1. Toyotaka Sakai, 2011. "A note on strategy-proofness from the doctor side in matching with contracts," Review of Economic Design, Springer, Springer, vol. 15(4), pages 337-342, December.
  2. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer, Springer, vol. 53(3), pages 561-589, August.

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