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Rationalizable implementation

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  • Bergemann, Dirk
  • Morris, Stephen
  • Tercieux, Olivier

Abstract

We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict version of the monotonicity condition introduced by Maskin is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive, i.e. in distinct states it selects distinct outcomes, we show that strict Maskin monotonicity is also sufficient under a mild "no worst alternative" condition. In particular, no economic condition is required. We discuss how our results extend when the social choice function is not responsive.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 3 (May)
Pages: 1253-1274

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:3:p:1253-1274

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Implementation Complete information Rationalizability Maskin monotonicity Robust mechanism design Robust implementation;

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References

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  1. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, 07.
  2. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
  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. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  5. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  6. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer, vol. 28(1), pages 111-125, January.
  7. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
  8. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity Of Mixed Equilibria In Mechanisms: A Unified Approach To Exact And Approximate Implementation," Working Papers wp2009_0908, CEMFI.
  9. 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.
  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. 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.
  12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  13. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  14. 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.
  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. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," CCES Discussion Paper Series 43, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
  2. Claudio Mezzetti & Ludovic Renou, 2012. "Implementation in Mixed Nash Equilibrium," Department of Economics - Working Papers Series 1146, The University of Melbourne.
  3. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Levine's Working Paper Archive 786969000000000187, David K. Levine.
  4. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
  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. 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.
  7. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
  8. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
  9. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.

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