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Nash implementation with lottery mechanisms

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Author Info
BOCHET, Olivier

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Abstract

Consider the problem of exact Nash Implementation of social choice correspondences. Define a lottery mechanism as a mechanism in which the planner can randomize on alternatives out of equilibrium while pure alternatives are always chosen in equilibrium. When preferences over alternatives are strict, we show that Maskin monotonicity (Maskin, 1999) is both necessary and sufficient for a social choice correspondence to be Nash implementable. We discuss how to relax the assumption of strict preferences. Next, we examine social choice correspondences with private components. Finally, we apply our method to the issue of voluntary implementation (Jackson and Palfrey, 2001).

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2005072.

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Date of creation: 01 Nov 2005
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Handle: RePEc:cor:louvco:2005072

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Related research
Keywords: lottery mechanism; Maskin monotonicity; no-veto power; Nash implementation;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, vol. 50(2), pages 285-299, April. [Downloadable!] (restricted)
  2. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October. [Downloadable!] (restricted)
  3. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January. [Downloadable!] (restricted)
  4. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February. [Downloadable!] (restricted)
  5. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
  6. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier. [Downloadable!] (restricted)
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  7. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September. [Downloadable!] (restricted)
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  8. Jackson, Matthew O. & Palfrey, Thomas R., 2001. "Voluntary Implementation," Journal of Economic Theory, Elsevier, vol. 98(1), pages 1-25, May. [Downloadable!] (restricted)
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    • Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dirk Bergemann & Stephen Morris, 2009. "Rationalizable Implementation," Cowles Foundation Discussion Papers 1697, Cowles Foundation, Yale University. [Downloadable!]
  2. Veiga, Helena & Vorsatz, Marc, 2006. "Price Manipulation in an Experimental Asset Market," Research Memoranda 024, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  3. Olivier, BOCHET & Franois, MANIQUET, 2006. "Virtual Nash implementation with admissible support," Discussion Papers (ECON - Département des Sciences Economiques) 2006043, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
    Other versions:
  4. Hannu Vartiainen, 2007. "Subgame perfect implementation of voting rules via randomized mechanisms," Social Choice and Welfare, Springer, vol. 29(3), pages 353-367, October. [Downloadable!] (restricted)
  5. Ashraf-Ball, Hezlin & Oswald, Andrew J. & Oswald, James I., 2009. "Hydrogen Transport and the Spatial Requirements of Renewable Energy," The Warwick Economics Research Paper Series (TWERPS) 903, University of Warwick, Department of Economics. [Downloadable!]
  6. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 902, University of Warwick, Department of Economics. [Downloadable!]
    Other versions:
  7. Hannu Vartiainen, 2007. "Nash implementation and the bargaining problem," Social Choice and Welfare, Springer, vol. 29(2), pages 333-351, September. [Downloadable!] (restricted)
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