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Monotonicity and Nash implementation in matching markets with contracts

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Author Info
Claus-Jochen Haake () (Institute of Mathematical Economics, Bielefeld University)
Bettina Klaus () (Department of Economics, Maastricht University)

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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
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File Function: First version, 2005
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Publisher Info
Paper provided by Bielefeld University, Institute of 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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Web page: http://www.imw.uni-bielefeld.de/
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Related research
Keywords: matching with contracts; (Maskin) monotonicity; Nash implementation; stability.;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation
J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Haake,Claus-Jochen & Klaus,Bettina, 2005. "Monotonicity and Nash Implementation in Matching Markets with Contracts," Research Memoranda 028, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  2. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January. [Downloadable!] (restricted)
  3. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 23-38, January. [Downloadable!] (restricted)
    Other versions:
  4. William Thomson, 1999. "Monotonic extensions on economic domains," Review of Economic Design, Springer, vol. 4(1), pages 13-33. [Downloadable!] (restricted)
    Other versions:
  5. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February. [Downloadable!] (restricted)
  6. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
  7. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
  8. Sonmez, Tayfun, 1996. "Implementation in generalized matching problems," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 429-439. [Downloadable!] (restricted)
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  9. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science. [Downloadable!]
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  10. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October. [Downloadable!] (restricted)
  11. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708. [Downloadable!] (restricted)
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  12. 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, vol. 84(4), pages 992-1044, September. [Downloadable!] (restricted)
  13. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation, Yale University. [Downloadable!]
  14. 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. [Downloadable!] (restricted)
  15. John W. Hatfield & Paul Milgrom, 2005. "Auctions, Matching and the Law of Aggregate Demand," Levine's Bibliography 122247000000000780, UCLA Department of Economics. [Downloadable!]
  16. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Society for Economic Theory, vol. 1(2), pages 233-273, June. [Downloadable!]
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  17. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
  20. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September. [Downloadable!] (restricted)
  21. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September. [Downloadable!]
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  22. Hurwicz, Leonid & Schmeidler, David, 1978. "Construction of Outcome Functions Guaranteeing Existence and Pareto Optimality of Nash Equilibria," Econometrica, Econometric Society, vol. 46(6), pages 1447-74, November. [Downloadable!] (restricted)
  23. Ehlers, Lars, 2004. "Monotonic and implementable solutions in generalized matching problems," Journal of Economic Theory, Elsevier, vol. 114(2), pages 358-369, February. [Downloadable!] (restricted)
  24. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Claus-Jochen Haake & Bettina Klaus, 2008. "Stability and Nash implementation in matching markets with couples," Working Papers 399, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
    Other versions:
  2. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2006. "Farsightedly Stable Networks," Research Memoranda 041, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  3. Claus-Jochen Haake & Bettina Klaus, 2009. "Monotonicity and Nash implementation in matching markets with contracts," Economic Theory, Springer, vol. 41(3), pages 393-410, December. [Downloadable!] (restricted)
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