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A robustness result for rationalizable implementation

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  • Di Tillio, Alfredo

Abstract

This paper investigates the extent to which rationalizable implementation depends on the implicit common knowledge restrictions usually embodied in traditional models. It is shown that under fairly general conditions such restrictions are without loss of generality in the following sense: If a mechanism implements a social choice function f on a type space X, then implements f assuming only that the agents' k-order beliefs are among those described by an open set B containing X, while higher-order beliefs are completely unrestricted. The result is applied to direct implementation on payoff type spaces, and related to the weak (incentive compatible) implementation problem.

Suggested Citation

  • Di Tillio, Alfredo, 2011. "A robustness result for rationalizable implementation," Games and Economic Behavior, Elsevier, vol. 72(1), pages 301-305, May.
    • Handle: RePEc:eee:gamebe:v:72:y:2011:i:1:p:301-305
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    References listed on IDEAS

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    1. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    2. 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..
    3. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
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    5. 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..
    6. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    7. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
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    Cited by:

    1. Takashi Kunimoto & Rene Saran & Roberto Serrano, 2020. "Interim Rationalizable Implementation of Functions," Working Papers 2020-23, Brown University, Department of Economics.
    2. de Clippel, Geoffroy & Saran, Rene & Serrano, Roberto, 2023. "Continuous level-k mechanism design," Games and Economic Behavior, Elsevier, vol. 140(C), pages 481-501.

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