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Bayesian and Dominant Strategy Implementation Revisited

Author

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  • Alex Gershkov
  • Benny Moldovanu
  • Xianwen Shi

Abstract

We consider a standard social choice environment with linear utility and one-dimensional types. We show by counterexample that, when there are at least three physical alternatives, Bayes-Nash Incentive Compatibility (BIC) and Dominant Strategy Incentive Compatibility (DIC) need no longer be equivalent. The example with three alternatives is minimal since we do obtain a general equivalence result for settings with only two social alternatives. Our negative result does not mathematically contradict the Manelli and Vincent (2010) equivalence obtained in a one-object auction setting, but it shows that BIC-DIC equivalence is only valid in restrictive environments. Our insights are based on mathematical results about the existence of monotone measures with given monotone marginals.

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2011. "Bayesian and Dominant Strategy Implementation Revisited," Working Papers tecipa-422, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-422
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    Citations

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    Cited by:

    1. Prokic-Breuer, T. & Dronkers, J., 2012. "The high performance of Dutch and Flemish 15-year-old native pupils: explaining country differences in math scores between highly stratified educational systems," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Yeon‐Koo Che & Jinwoo Kim & Konrad Mierendorff, 2013. "Generalized Reduced‐Form Auctions: A Network‐Flow Approach," Econometrica, Econometric Society, vol. 81(6), pages 2487-2520, November.
    3. Csapó, Gergely & Müller, Rudolf, 2013. "Optimal mechanism design for the private supply of a public good," Games and Economic Behavior, Elsevier, vol. 80(C), pages 229-242.
    4. Jacob K. Goeree & Alexey Kushnir, 2011. "On the equivalence of Bayesian and dominant strategy implementation in a general class of social choice problems," ECON - Working Papers 021, Department of Economics - University of Zurich.
    5. Jacob K. Goeree & Alexey Kushnir, 2011. "A geometric approach to mechanism design," ECON - Working Papers 056, Department of Economics - University of Zurich, revised Jun 2013.

    More about this item

    Keywords

    Bayesian Implementation; Dominant Strategy Implementation; Equivalence;

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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