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Rationalizable Implementation

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Abstract

This note studies (full) implementation of social choice functions under complete information in (correlated) rationalizable strategies. The monotonicity condition shown by Maskin (1999) to be necessary for Nash implementation is also necessary under the more stringent solution concept. We show that it is also sufficient under a mild "no worst alternative" condition. In particular, no economic condition is required.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1697.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1697.

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Length: 21 pages
Date of creation: May 2009
Date of revision:
Publication status: Published in Journal of Economic Theory (May 2011), 146(3): 1253–1274
Handle: RePEc:cwl:cwldpp:1697

Note: CFP 1328
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Implementation; Complete information; Rationalizability; Maskin monotonicity;

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References

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  1. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
  3. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers 1666, Cowles Foundation for Research in Economics, Yale University.
  4. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 902, University of Warwick, Department of Economics.
  5. 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.
  6. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, 07.
  7. 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.
  8. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  9. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  10. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
  11. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  12. 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.
  13. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  14. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  15. 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.
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Citations

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Cited by:
  1. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
  2. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
  3. Claudio Mezzetti & Ludovic Renou, 2009. "Implementation in Mixed Nash Equilibrium," Discussion Papers in Economics 09/10, Department of Economics, University of Leicester, revised Jan 2010.
  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. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Levine's Working Paper Archive 122247000000002286, David K. Levine.
  6. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
  7. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
  8. 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.
  9. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.

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