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Rationalizable Implementation

Author

Listed:
  • Dirk Bergemann

    (Department Economics - Yale University - Yale University [New Haven])

  • Stephen Morris

    (Department of Economics - Princeton University - Princeton University)

  • Olivier Tercieux

    (PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

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.

Suggested Citation

  • Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2011. "Rationalizable Implementation," Post-Print halshs-00654687, HAL.
  • Handle: RePEc:hal:journl:halshs-00654687
    DOI: 10.1016/j.jet.2010.12.011
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00654687
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    References listed on IDEAS

    as
    1. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
    2. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404 World Scientific Publishing Co. Pte. Ltd..
    3. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    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. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    6. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
    7. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    8. 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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    11. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
    12. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
    13. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    14. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    15. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    16. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    17. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    18. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    19. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
    20. 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.
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    22. 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.
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    Cited by:

    1. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404 World Scientific Publishing Co. Pte. Ltd..
    2. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
    3. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    4. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    5. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    6. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    7. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    8. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    9. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    10. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    11. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    12. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
    13. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.
    14. Chen, Yi-Chun & Sun, Yifei, 2015. "Full implementation in backward induction," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 71-76.
    15. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    16. Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2014. "Mechanism Design with Bounded Depth of Reasoning and Small Modeling Mistakes," Working Papers 2014-7, Brown University, Department of Economics.
    17. Kimya, Mert, 2017. "Nash implementation and tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 102(C), pages 138-146.

    More about this item

    Keywords

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

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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