On the Equivalence of Bayesian and Dominant Strategy Implementation

Authors

  • Alex Gershkov,

    1. Faculty of Social Science, Hebrew University of Jerusalem, Mount Scopus, 91905 Jerusalem, Israel; alexg@huji.ac.il
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  • Jacob K. Goeree,

    1. Chair for Organization Design, Dept. of Economics, University of Zürich, Blümlisalpstrasse 10, CH-8006 Zürich, Switzerland; jacob.goeree@econ.uzh.ch
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  • Alexey Kushnir,

    1. Chair for Organization Design, Dept. of Economics, University of Zürich, Blümlisalpstrasse 10, CH-8006 Zürich, Switzerland; alexey.kushnir@econ.uzh.ch
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  • Benny Moldovanu,

    1. Microeconomics, University of Bonn, Lennéstr. 37, 53113 Bonn, Germany; mold@uni-bonn.de
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  • Xianwen Shi

    1. Dept. of Economics, University of Toronto, 150 St. George Street, Toronto, Ontario M5S 3G7, Canada; xianwen.shi@utoronto.ca
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    • The present study builds on the insights of two papers: Gershkov, Moldovanu, and Shi (2011) uncovered the role of a theorem due to Gutmann et al. (1991) for the analysis of mechanism equivalence, and Goeree and Kushnir (2011) generalized the theorem to several functions, thus greatly widening its applicability. Goeree and Kushnir gratefully acknowledge financial support from the European Research Council (ERC Advanced Investigator Grant ESEI-249433). Moldovanu wishes to thank the German Science Foundation and the European Research Council for financial support, and Shi acknowledges financial support from the Canadian SSHRC under a standard research grant. We would like to thank Christian Ewerhart, Sergiu Hart, Angel Hernando-Veciana, Philippe Jehiel, Nenad Kos, John Ledyard, Konrad Mierendorff, Rudolf Müller, Nick Netzer, Phil Reny, Jean-Charles Rochet, Ennio Stacchetti, Thomas Tröger, the editors, and anonymous referees, as well as various seminar participants for useful suggestions.


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, Kemperman, Reeds, and Shepp (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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