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Rationalizable Implementation

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  • Dirk Bergemann
  • Stephen Morris
  • Olivier Tercieux

Abstract

We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict (and thus stronger) version of the monotonicity condition introduced by Maskin (1999) is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive (i.e., it never selects the same outcome in two distinct states), we show that it is also sufficient under a mild "no worst alternative" condition. In particular, no economic condition is required. We also discuss how our results extend when the social choice function is not responsive.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 661465000000000022.

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Date of creation: 17 Mar 2010
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Handle: RePEc:cla:levarc:661465000000000022

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References

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  1. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
  2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, November.
  3. Abreu, D. & Matsushima, H., 1991. "Virtual Implementation in Iteratively Undominated Strategies: Incomplete Information," Working Papers e-91-2, Hoover Institution, Stanford University.
  4. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics.
  5. Dirk Bergemann & Stephen Morris, 2010. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 661465000000000017, David K. Levine.
  6. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  7. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
  8. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Roberto Serrano & Antonio Cabrales, 2007. "Implemetation In Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
  10. 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.
  11. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Working Papers 2009-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  12. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  13. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
  14. Marion Oury & Olivier Tercieux, 2009. "Continuous Implementation," Economics Working Papers 0090, Institute for Advanced Study, School of Social Science.
  15. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
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Cited by:
  1. Ludovic Renou & Karl H. Schlag, 2009. "Implementation in Minimax Regret Equilibrium," Discussion Papers in Economics 09/24, Department of Economics, University of Leicester.
  2. Makoto Shimoji & Paul Schweinzer, 2012. "Implementation without Incentive Compatibility: Two Stories with Partially Informed Planners," Discussion Papers 12/21, Department of Economics, University of York.
  3. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
  4. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
  5. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
  6. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 122247000000002286, David K. Levine.
  7. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
  8. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.

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