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Robust Implementation in Direct Mechanisms

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

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  • Dirk Bergemann
  • Stephen Morris

Abstract

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice for all beliefs at every type profile. In an interdependent value environment with single crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust implementation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones.The contraction property requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having an eigenvalue less than one.

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  • 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..
  • Handle: RePEc:wsi:wschap:9789814374590_0004
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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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