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Rationalizable Implementation

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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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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1697-r.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 1697R.

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Length: 29 pages
Date of creation: Jan 2010
Date of revision:
Publication status: Published in Journal of Economic Theory (May 2011), 146(3): 1253–1274
Handle: RePEc:cwl:cwldpp:1697r

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. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  2. 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.
  3. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, 07.
  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. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
  6. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
  7. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  8. 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.
  9. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  10. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  11. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  12. 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.
  13. 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.
  14. BOCHET, Olivier, 2005. "Nash implementation with lottery mechanisms," CORE Discussion Papers 2005072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. 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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Citations

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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. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," Discussion Paper Series 555, Institute of Economic Research, Hitotsubashi University.
  3. Claudio Mezzetti & Ludovic Renou, 2012. "Implementation in Mixed Nash Equilibrium," Department of Economics - Working Papers Series 1146, The University of Melbourne.
  4. 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.
  5. Dirk Bergemann & Stephen Morris, 2008. "Robust Implementation in General Mechanisms," Cowles Foundation Discussion Papers 1666R, Cowles Foundation for Research in Economics, Yale University, revised Jan 2010.
  6. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
  7. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
  8. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
  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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