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Robust Implementation: The Role of Large Type Spaces

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Author Info
Dirk Bergemann () (Cowles Foundation, Yale University)
Stephen Morris

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Abstract

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with a social choice function. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly stronger than both Maskin monotonicity (necessary and almost sufficient for complete information implementation) and ex post monotonicity (necessary and almost sufficient for ex post implementation). It is equivalent to Bayesian monotonicity on all type spaces. It requires that there not be too much interdependence of types. We characterize robust monotonicity for some interesting economic environments. We identify conditions where, if robust implementation is possible, it is possible in a direct mechanism. We identify conditions where, if robust implementation is not possible, virtual robust implementation is not possible either.

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File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1519.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1519.

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Length: 59 pages
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:cwl:cwldpp:1519

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Mechanism Design; Implementation; Robustness; Common Knowledge; Interim Equilibrium; Iterative Deletion; Dominant Strategies;

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Find related papers by JEL classification:
C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

References listed on IDEAS
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  1. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. [Downloadable!] (restricted)
  2. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Harvard Institute of Economic Research Working Papers 2064, Harvard - Institute of Economic Research. [Downloadable!]
    Other versions:
  3. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February. [Downloadable!] (restricted)
    Other versions:
  4. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-91, June. [Downloadable!] (restricted)
  5. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421R, Cowles Foundation, Yale University, revised Apr 2004. [Downloadable!]
    Other versions:
  6. 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. [Downloadable!] (restricted)
  7. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  8. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
  9. repec:bep:theadv:v:3:y:2003:i:1:p:1073-1073 is not listed on IDEAS
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  10. Battigalli, P., 1999. "Rationalizability in Incomplete Information Games," Economics Working Papers eco99/17, European University Institute.
  11. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November. [Downloadable!] (restricted)
  12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September. [Downloadable!] (restricted)
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Rafael Hortala-Vallve, 2007. "Inefficiencies on Linking Decisions," Economics Series Working Papers 321, University of Oxford, Department of Economics. [Downloadable!]
  2. Dirk Bergemann & Stephen Morris, 2007. "Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609RR, Cowles Foundation, Yale University, revised Jan 2009. [Downloadable!]
    Other versions:
  3. Hitoshi Matsushima, 2004. "Non-Consequential Moral Preferences, Detail-Free Implementation, and Representative Systems," CIRJE F-Series CIRJE-F-304, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  4. Tatsuyoshi Saijo & Tomas Sjostrom & Takehiko Yamato, 2005. "Secure Implementation," Economics Working Papers 0056, Institute for Advanced Study, School of Social Science. [Downloadable!]
    Other versions:
  5. 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. [Downloadable!]
    Other versions:
  6. Dirk Bergemann & Stephen Morris, 2006. "Ex Post Implementation," Levine's Bibliography 122247000000001110, UCLA Department of Economics. [Downloadable!]
    Other versions:
  7. Takashi Kunimoto, 2006. "The Robustness Of Equilibrium Analysis: The Case Of Undominated Nash Equilibrium," Departmental Working Papers 2006-26, McGill University, Department of Economics. [Downloadable!]
  8. Hitoshi Matsushima, 2004. "On Detail-Free Mechanism Design and Rationality," CIRJE F-Series CIRJE-F-287, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  9. Hitoshi Matsushima, 2007. "Detail-Free Mechanism Design in Twice Iterative Dominance: Large Economies," CIRJE F-Series CIRJE-F-519, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  10. Pierpaolo Battigalli, 2004. "Rationalization in Signaling Games: Theory and Applications," Working Papers 275, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
    Other versions:
  11. Pierpaolo Battigalli & Alfredo Di Tillio & Edoardo Grillo & Antonio Penta, 2008. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," Working Papers 340, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
  12. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421R, Cowles Foundation, Yale University, revised Apr 2004. [Downloadable!]
    Other versions:
  13. Yi-Chun Chen & Ngo Van Long & Xiao Luo, 2007. "Iterated Strict Dominance in General Games," CIRANO Working Papers 2007s-03, CIRANO. [Downloadable!]
    Other versions:
  14. Dirk Bergemann & Stephen Morris, 2007. "Strategic Distinguishability and Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609R, Cowles Foundation, Yale University, revised Apr 2008. [Downloadable!]
  15. Stephen Morris & Dirk Bergemann, 2007. "Strategic Distinguishability With an Application to Robust Virtual Implementation," Levine's Bibliography 843644000000000149, UCLA Department of Economics. [Downloadable!]
    Other versions:
  16. Hideki Mizukami & Takuma Wakayama, 2004. "Dominant Strategy Implementation in Pure Exchange Economies," Discussion Papers in Economics and Business 04-03-Rev, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP), revised Mar 2005. [Downloadable!]
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