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The Role of the Common Prior in Robust Implementation

In: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs

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  • Dirk Bergemann
  • Stephen Morris

Abstract

We consider the role of the common prior for robust implementation in an environment with interdependent values. Specifically, we investigate a model of public good provision which allows for negative and positive informational externalities. In the corresponding direct mechanism, the agents’ reporting strategies are strategic complements with negative informational externalities and strategic substitutes with positive informational externalities. We derive the necessary and sufficient conditions for robust implementation in common prior type spaces and contrast this with our earlier results without the common prior. In the case of strategic complements the necessary and sufficient conditions for robust implementation do not depend on the existence of a common prior. In contrast, with strategic substitutes, the implementation conditions are much weaker under the common prior assumption.

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  • Dirk Bergemann & Stephen Morris, 2012. "The Role of the Common Prior in Robust Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 6, pages 241-251, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814374590_0006
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    References listed on IDEAS

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    1. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    2. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    3. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    4. 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..
    5. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," LIDAM Discussion Papers CORE 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Dirk Bergemann & Stephen Morris, 2007. "Strategic Distinguishability with an Application to Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609, Cowles Foundation for Research in Economics, Yale University.
    7. Dirk Bergemann & Juuso Valimaki, 2002. "Information Acquisition and Efficient Mechanism Design," Econometrica, Econometric Society, vol. 70(3), pages 1007-1033, May.
    8. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(2), pages 223-227.
    9. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(2), pages 341-388.
    10. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    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. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    3. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    4. Che, Yeon-Koo & Kim, Jinwoo & Kojima, Fuhito, 2015. "Efficient assignment with interdependent values," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 54-86.

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    More about this item

    Keywords

    Mechanism Design; Game Theory; Auction Theory; Implementation; Private Information; First and Higher-Order Belief; BayesNash Equilibrium; Ex Post Equilibrium; Rationalizability; Vickrey-Clarke-Groves Mechanisms; Private Value; Interdependent Value; Common Value; Belief-Free Mechanisms;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D0 - Microeconomics - - General

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