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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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  • Dirk Bergemann & Stephen Morris, 2009. "Rationalizable Implementation," Cowles Foundation Discussion Papers 1697, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1697
    Note: CFP 1328
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    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. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    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," The Review of Economic Studies, Review of Economic Studies Ltd, 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. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    8. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    9. 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.
    10. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    11. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    12. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    13. Barnett,William A. & Moulin,Hervé & Salles,Maurice & Schofield,Norman J. (ed.), 1995. "Social Choice, Welfare, and Ethics," Cambridge Books, Cambridge University Press, number 9780521443401, September.
    14. 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.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    16. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    17. 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.
    18. 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.
    19. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    20. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    21. 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.
    22. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    23. 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.
    24. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 41-54, December.
    25. 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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    More about this item

    Keywords

    Implementation; Complete information; Rationalizability; Maskin monotonicity;
    All these keywords.

    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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