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On Maskin monotonicity of solution based social choice rules

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  • Claus-Jochen Haake

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Walter Trockel

    ()
    (Institute of Mathematical Economics, Bielefeld University)

Abstract

Howard (1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by de.ning a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even su.cient for Nash implementability.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-393.pdf
File Function: First version, 2007
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 393.

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Length: 11 pages
Date of creation: Jul 2007
Date of revision:
Handle: RePEc:bie:wpaper:393

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Keywords: Maskin monotonicity; social choice rule; bargaining games; Nash program; mechanism; implementation;

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References

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  1. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  2. Trockel,W., 1999. "Integrating the Nash program into mechanism theory," Working Papers, Bielefeld University, Center for Mathematical Economics 305, Bielefeld University, Center for Mathematical Economics.
  3. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, Elsevier, vol. 4(3), pages 484-492, July.
  4. Nir Dagan & Roberto Serrano, 1997. "Invariance and randomness in the Nash program for coalitional games," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 217, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Trockel,W., 1999. "Unique Nash implementation for a class of bargaining solutions," Working Papers, Bielefeld University, Center for Mathematical Economics 308, Bielefeld University, Center for Mathematical Economics.
  6. Serrano, Roberto, 1997. "A comment on the Nash program and the theory of implementation," Economics Letters, Elsevier, Elsevier, vol. 55(2), pages 203-208, August.
  7. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, Elsevier, vol. 56(1), pages 142-159, February.
  8. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  9. Trockel,W., 2001. "Can and should the Nash program be looked at as a part of mechanism theory?," Working Papers, Bielefeld University, Center for Mathematical Economics 322, Bielefeld University, Center for Mathematical Economics.
  10. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer, Springer, vol. 1(1), pages 1-14, December.
  12. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer, Springer, vol. 16(2), pages 277-294.
  13. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, Econometric Society, vol. 21(1), pages 128-140, April.
  14. Damme, E.E.C. van, 1986. "The Nash bargaining solution is optimal," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154426, Tilburg University.
  15. Roberto Serrano, 2007. "Nash program," Working Papers, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales 2007-05, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  16. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, Elsevier, vol. 86(1), pages 50-76, May.
  17. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, Elsevier, vol. 62(1), pages 23-28, January.
  18. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(1), pages 78-100, February.
  19. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 43-56, January.
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Citations

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Cited by:
  1. Trockel, Walter, 2011. "An exact non-cooperative support for the sequential Raiffa solution," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 77-83, January.
  2. Claus-Jochen Haake, 2005. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Working Papers, Bielefeld University, Center for Mathematical Economics 366, Bielefeld University, Center for Mathematical Economics.

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