IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v146y2011i3p1253-1274.html
   My bibliography  Save this article

Rationalizable implementation

Author

Listed:
  • 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.

Suggested Citation

  • Bergemann, Dirk & Morris, Stephen & Tercieux, Olivier, 2011. "Rationalizable implementation," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1253-1274, May.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:3:p:1253-1274
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000044
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    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. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    3. 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..
    4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    5. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    6. 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.
    7. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
    8. 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.
    9. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    10. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    11. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Review of Economic Studies, Oxford University Press, vol. 76(4), pages 1175-1204.
    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. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    14. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    15. 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..
    16. 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.
    17. Abreu Dilip & Matsushima Hitoshi, 1994. "Exact Implementation," Journal of Economic Theory, Elsevier, vol. 64(1), pages 1-19, October.
    18. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    19. 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.
    20. 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.
    21. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    22. 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.
    23. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    8. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    9. Corbae, Dean & Marimon, Ramon, 2011. "Introduction to Incompleteness and Uncertainty in Economics," Journal of Economic Theory, Elsevier, vol. 146(3), pages 775-784, May.
    10. 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.
    11. Saran, Rene, 2016. "Bounded depths of rationality and implementation with complete information," Journal of Economic Theory, Elsevier, vol. 165(C), pages 517-564.
    12. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    13. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:146:y:2011:i:3:p:1253-1274. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.