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On the Equivalence of Bayesian and Dominant Strategy Implementation

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  • Alex Gershkov
  • Jacob Goeree
  • Alexey Kushnir
  • Benny Moldovanu
  • Xianwen Shi

Abstract

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann et al. (Annals of Probability, 1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed, or when the equivalence concept is strengthened to apply to interim expected allocations.

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Bibliographic Info

Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-445.

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Length: Unknown pages
Date of creation: 16 Feb 2012
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Handle: RePEc:tor:tecipa:tecipa-445

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Keywords: Bayesian Implementation; Dominant Strategy Implementation; Equivalence;

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  1. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421, Cowles Foundation for Research in Economics, Yale University.
  2. Muller, Rudolf & Perea, Andres & Wolf, Sascha, 2007. "Weak monotonicity and Bayes-Nash incentive compatibility," Games and Economic Behavior, Elsevier, vol. 61(2), pages 344-358, November.
  3. Hernando-Veciana, Ángel & Michelucci, Fabio, 2011. "Second best efficiency and the English auction," Games and Economic Behavior, Elsevier, vol. 73(2), pages 496-506.
  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.
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Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. “On the Equivalence of Bayesian and Dominant Strategy Implementation,” A. Gershkov et al (2012)
    by afinetheorem in A Fine Theorem on 2013-01-27 23:25:20
  2. “On the Equivalence of Bayesian and Dominant Strategy Implementation,” A. Gershkov et al (2012)
    by afinetheorem in A Fine Theorem on 2013-01-27 23:25:20
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Cited by:
  1. Rahul Deb & Mallesh Pai, 2013. "Symmetric Auctions," Working Papers tecipa-486, University of Toronto, Department of Economics.
  2. 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.
  3. Hitoshi Matsushima, 2012. "Optimal Multiunit Exchange Design with Single-Dimensionality," CARF F-Series CARF-F-292, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2012.
  4. Blumrosen, Liad & Feldman, Michal, 2013. "Mechanism design with a restricted action space," Games and Economic Behavior, Elsevier, vol. 82(C), pages 424-443.
  5. Debasis Mishra & Abdul Quadir, 2012. "Deterministic single object auctions with private values," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 12-06, Indian Statistical Institute, New Delhi, India.
  6. Kleiner, Andreas & Drexl, Moritz, 2013. "Why Voting? A Welfare Analysis," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79886, Verein für Socialpolitik / German Economic Association.
  7. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2013. "Optimal Mechanism Design without Money," Working Papers tecipa-481, University of Toronto, Department of Economics.
  8. Farinha Luz, Vitor, 2013. "Surplus extraction with rich type spaces," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2749-2762.

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