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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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    1. 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.
    2. Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences.
    3. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
    4. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    5. Palfrey, Thomas R & Srivastava, Sanjay, 1991. "Nash Implementation Using Undominated Strategies," Econometrica, Econometric Society, vol. 59(2), pages 479-501, March.
    6. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer, vol. 9(2), pages 197-218.
    7. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer, vol. 18(4), pages 655-708.
    8. Eric Maskin, 1998. "Nash Equilibrium and Welfare Optimality," Harvard Institute of Economic Research Working Papers 1829, Harvard - Institute of Economic Research.
    9. M. Sanver, 2006. "Nash implementing non-monotonic social choice rules by awards," Economic Theory, Springer, vol. 28(2), pages 453-460, 06.
    10. Eric Maskin & John Moore, 1999. "Implementation and Renegotiation," Harvard Institute of Economic Research Working Papers 1863, Harvard - Institute of Economic Research.
    11. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
    12. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    13. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    14. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer, vol. 14(4), pages 513-525.
    15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    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. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
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