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Robust Implementation: The Role of Large Type Spaces

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  • Dirk Bergemann
  • Stephen Morris

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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Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
  • Handle: RePEc:cla:levrem:784828000000000116
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    References listed on IDEAS

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    6. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
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    8. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    9. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005. "Interim Rationalizability," Levine's Bibliography 666156000000000526, UCLA Department of Economics.
    10. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    11. Battigalli, P., 1999. "Rationalizability in Incomplete Information Games," Economics Working Papers eco99/17, European University Institute.
    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. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    14. 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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    Cited by:

    1. 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..
    2. Matsushima, Hitoshi, 2008. "Detail-free mechanism design in twice iterative dominance: Large economies," Journal of Economic Theory, Elsevier, vol. 141(1), pages 134-151, July.
    3. Chen, Yi-Chun & Long, Ngo Van & Luo, Xiao, 2007. "Iterated strict dominance in general games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 299-315, November.
    4. Dirk Bergemann & Stephen Morris, 2012. "Ex Post Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 3, pages 97-152, World Scientific Publishing Co. Pte. Ltd..
    5. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    6. Rafael Hortala-Vallve, 2010. "Inefficiencies on linking decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(3), pages 471-486, March.
    7. Pierpaolo Battigalli, 2006. "Rationalization In Signaling Games: Theory And Applications," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 67-93.
    8. , & , & ,, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    9. Cappelletti Giuseppe, 2010. "A Note on Rationalizability and Restrictions on Beliefs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-13, September.
    10. 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.
    11. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    12. Stephen Morris & Dirk Bergemann, 2007. "Strategic Distinguishability With an Application to Robust Virtual Implementation," Levine's Bibliography 843644000000000149, UCLA Department of Economics.
    13. Hideki Mizukami & Takuma Wakayama, 2004. "Dominant Strategy Implementation in Pure Exchange Economies," Discussion Papers in Economics and Business 04-03, Osaka University, Graduate School of Economics.
    14. Mizukami, Hideki & Wakayama, Takuma, 2007. "Dominant strategy implementation in economic environments," Games and Economic Behavior, Elsevier, vol. 60(2), pages 307-325, August.
    15. Dirk Bergemann & Stephen Morris, 2007. "Strategic Distinguishability and Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2008.
    16. Takashi Kunimoto, 2006. "The Robustness Of Equilibrium Analysis: The Case Of Undominated Nash Equilibrium," Departmental Working Papers 2006-26, McGill University, Department of Economics.

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    More about this item

    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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