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Nash implementation without no-veto power

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  • Benoît, Jean-Pierre
  • Ok, Efe A.
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/inca/622836

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    References

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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. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    3. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
    4. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    5. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
    6. Eric Maskin & John Moore, 1999. "Implementation and Renegotiation," Harvard Institute of Economic Research Working Papers 1863, Harvard - Institute of Economic Research.
    7. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
    8. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    11. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
    12. Jackson, Matthew O. & Palfrey, Thomas R., 2001. "Voluntary Implementation," Journal of Economic Theory, Elsevier, vol. 98(1), pages 1-25, May.
    13. 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.
    14. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    15. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    16. 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.
    17. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
    18. M. Sanver, 2006. "Nash implementing non-monotonic social choice rules by awards," Economic Theory, Springer, vol. 28(2), pages 453-460, 06.
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