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Nash implementation without no-veto power

  • Benoît, Jean-Pierre
  • Ok, Efe A.
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    For a society that consists of at least three individuals, we show that a social choice rule is Maskin monotonic if and only if it is Nash implementable by means of a mechanism that is stochastic or a mechanism that contains (arbitrary) awards. In equilibrium, the mechanisms do not have any stochastic elements and do not involve any awards. Thus, loosely speaking, one can drop the no-veto power postulate from Maskin's classic theorem on Nash implementability, provided that the notion of a mechanism is suitably generalized, thereby narrowing the gap between the properties of Maskin monotonicity and Nash implementability. Moreover, using the standard notion of a mechanism, we prove that Nash implementability is equivalent to Maskin monotonicity with renegotiation: this is a pure improvement over a well-known result of Maskin and Moore [Maskin, E., Moore, J., 1999. Implementation and renegotiation, Rev. Econ. Studies 66, 39-56].

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    File URL: http://www.sciencedirect.com/science/article/B6WFW-4RKTNCM-4/2/1068a9b12846aa89d8516f9a020dce0b
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    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 64 (2008)
    Issue (Month): 1 (September)
    Pages: 51-67

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    Handle: RePEc:eee:gamebe:v:64:y:2008:i:1:p:51-67
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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    1. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
    2. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    4. Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences.
    5. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
    6. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    9. M. Sanver, 2006. "Nash implementing non-monotonic social choice rules by awards," Economic Theory, Springer, vol. 28(2), pages 453-460, 06.
    10. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
    11. Eric Maskin & John Moore, 1998. "Implementation and renegotiation," LSE Research Online Documents on Economics 19350, London School of Economics and Political Science, LSE Library.
    12. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    13. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    14. Benoit, Jean-Pierre & Ok, Efe A., 2006. "Maskin's Theorem with limited veto power," Games and Economic Behavior, Elsevier, vol. 55(2), pages 331-339, May.
    15. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
    16. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
    17. Shinotsuka, Tomoichi & Takamiya, Koji, 2003. "The weak core of simple games with ordinal preferences: implementation in Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 44(2), pages 379-389, August.
    18. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
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