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Nash implementation with lottery mechanisms

  • BOCHET, Olivier

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: 00 Nov 2005
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Handle: RePEc:cor:louvco:2005072
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  1. Maskin, Eric & Sjostrom, Tomas, 2001. "Implementation Theory," Working Papers 5-01-1, Pennsylvania State University, Department of Economics.
  2. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
  3. 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.
  4. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  5. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
  6. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  7. Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March.
  9. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  10. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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