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On Maskin monotonicity of solution based social choice rules

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  • Claus-Jochen Haake
  • Walter Trockel

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 defining 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 sufficient for Nash implementability.
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  • Claus-Jochen Haake & Walter Trockel, 2010. "On Maskin monotonicity of solution based social choice rules," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 17-25, March.
    • Handle: RePEc:spr:reecde:v:14:y:2010:i:1:p:17-25
    DOI: 10.1007/s10058-008-0062-7
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    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
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    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    5. Roberto Serrano, 2007. "Nash program," Working Papers 2007-05, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
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    7. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    8. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    9. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    10. Eric van Damme, 1984. "The Nash Bargaining Solution is Optimal," Discussion Papers 597, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Moulin, H., 1984. "Implementing the Kalai-Smorodinsky bargaining solution," Journal of Economic Theory, Elsevier, vol. 33(1), pages 32-45, June.
    12. Damme, Eric van, 1986. "The Nash bargaining solution is optimal," Journal of Economic Theory, Elsevier, vol. 38(1), pages 78-100, February.
    13. Bergin, James & Duggan, John, 1999. "An Implementation-Theoretic Approach to Non-cooperative Foundations," Journal of Economic Theory, Elsevier, vol. 86(1), pages 50-76, May.
    14. Leonid Hurwicz, 1994. "Economic design, adjustment processes, mechanisms, and institutions," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 1-14, December.
    15. Trockel, Walter, 2017. "Can and should the Nash Program be looked at as a part of mechanism theory," Center for Mathematical Economics Working Papers 322, Center for Mathematical Economics, Bielefeld University.
    16. Haake, Claus-Jochen, 2017. "Implementation of the Kalai Smorodinski bargaining solution in dominant strategies," Center for Mathematical Economics Working Papers 301, Center for Mathematical Economics, Bielefeld University.
    17. Howard, J. V., 1992. "A social choice rule and its implementation in perfect equilibrium," Journal of Economic Theory, Elsevier, vol. 56(1), pages 142-159, February.
    18. Trockel, Walter, 2017. "Unique Nash implementation for a class of bargaining solutions," Center for Mathematical Economics Working Papers 308, Center for Mathematical Economics, Bielefeld University.
    19. Naeve, Jorg, 1999. "Nash implementation of the Nash bargaining solution using intuitive message spaces," Economics Letters, Elsevier, vol. 62(1), pages 23-28, January.
    20. Walter Trockel, 2000. "Implementations of the Nash solution based on its Walrasian characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 277-294.
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    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 & Walter Trockel, 2020. "Introduction to the Special Issue “Bargaining”," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 1-6, November.
    3. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    4. Haake, Claus-Jochen & Trockel, Walter, 2021. "Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium," Center for Mathematical Economics Working Papers 647, Center for Mathematical Economics, Bielefeld University.
    5. Claus-Jochen Haake & Walter Trockel, 2022. "Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 635-649, December.
    6. Haake, Claus-Jochen, 2009. "Two support results for the Kalai-Smorodinsky solution in small object division markets," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 177-187, March.
    7. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    8. Claus-Jochen Haake & Walter Trockel, 2021. "Socio-legal Systems and Implementation of the Nash Solution in Debreu-Hurwicz Equilibrium," Working Papers CIE 140, Paderborn University, CIE Center for International Economics.

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    More about this item

    Keywords

    Maskin monotonicity; Social choice rule; Bargaining games; Nash program; Mechanism; Implementation; C71; C78; D61;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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