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Nash Implementation with Lottery Mechanisms

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  • Olivier Bochet

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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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File URL: http://hdl.handle.net/10.1007/s00355-006-0158-3
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 28 (2007)
Issue (Month): 1 (January)
Pages: 111-125

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Handle: RePEc:spr:sochwe:v:28:y:2007:i:1:p:111-125

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  1. Vartiainen, Hannu, 2007. "Subgame perfect implementation: A full characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 111-126, March.
  2. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
  3. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  4. 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.
  5. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  6. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
  7. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  8. Jackson, Matthew O. & Palfrey, Thomas R., 1999. "Voluntary Implementation," Working Papers 1077, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-99, September.
  10. Kara, Tarik & Sonmez, Tayfun, 1996. "Nash Implementation of Matching Rules," Journal of Economic Theory, Elsevier, vol. 68(2), pages 425-439, February.
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