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On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types

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  • Alexey Kushnir

Abstract

We consider general social choice environments with private values and correlated types. Each agent's matrix of conditional probabilities satisfies the full rank condition. We show that for any Bayesian incentive compatible mechanism there exists a dominant strategy incentive compatible mechanism that delivers the same interim expected utilities to all agents and generates at least the same social surplus. In addition, if there is a social alternative that is inferior to the other alternatives for all agents the dominant strategy incentive compatible mechanism matches exactly the social surplus. These results extend to environments with interdependent values satisfying the single crossing condition.

Suggested Citation

  • Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
  • Handle: RePEc:zur:econwp:129
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    File URL: http://www.econ.uzh.ch/static/wp/econwp129.pdf
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    References listed on IDEAS

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    1. Barelli, Paulo, 2009. "On the genericity of full surplus extraction in mechanism design," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1320-1332, May.
    2. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-438, March.
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    5. Mookherjee, Dilip & Reichelstein, Stefan, 1992. "Dominant strategy implementation of Bayesian incentive compatible allocation rules," Journal of Economic Theory, Elsevier, vol. 56(2), pages 378-399, April.
    6. McAfee, R Preston & McMillan, John & Reny, Philip J, 1989. "Extracting the Surplus in the Common-Value Auction," Econometrica, Econometric Society, vol. 57(6), pages 1451-1459, November.
    7. Robert, Jacques, 1991. "Continuity in auction design," Journal of Economic Theory, Elsevier, vol. 55(1), pages 169-179, October.
    8. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
    9. 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.
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    Citations

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    Cited by:

    1. Goeree, Jacob K. & Kushnir, Alexey, 2016. "Reduced form implementation for environments with value interdependencies," Games and Economic Behavior, Elsevier, vol. 99(C), pages 250-256.
    2. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.
    3. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
    4. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "Stochastic Dominance Under Independent Noise," Papers 1807.06927, arXiv.org, revised Sep 2018.
    5. repec:oup:restud:v:84:y:2017:i:2:p:688-717. is not listed on IDEAS
    6. Jarman, Felix & Meisner, Vincent, 2017. "Deterministic Mechanisms, the Revelation Principle, and Ex-Post Constraints," Rationality and Competition Discussion Paper Series 32, CRC TRR 190 Rationality and Competition.
    7. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    8. repec:eee:ecolet:v:161:y:2017:i:c:p:96-98 is not listed on IDEAS
    9. repec:eee:gamebe:v:105:y:2017:i:c:p:9-39 is not listed on IDEAS
    10. Jarman, Felix & Meisner, Vincent, 2017. "Ex-post optimal knapsack procurement," Journal of Economic Theory, Elsevier, vol. 171(C), pages 35-63.
    11. Steven J. Brams & Todd R. Kaplan & D. Marc Kilgour, 2015. "A Simple Bargaining Mechanism that Elicits Truthful Reservation Prices," Group Decision and Negotiation, Springer, vol. 24(3), pages 401-413, May.
    12. Drexl, Moritz & Kleiner, Andreas, 2015. "Optimal private good allocation: The case for a balanced budget," Games and Economic Behavior, Elsevier, vol. 94(C), pages 169-181.
    13. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    14. Yu Chen, 2017. "Simplification of Contracting under Adverse Selection with Ex Post State," Graz Economics Papers 2017-01, University of Graz, Department of Economics.
    15. Hernando-Veciana, Ángel & Michelucci, Fabio, 2014. "On the optimality of not allocating," Economics Letters, Elsevier, vol. 125(2), pages 233-235.
    16. Koessler, Frédéric & Skreta, Vasiliki, 2016. "Informed seller with taste heterogeneity," Journal of Economic Theory, Elsevier, vol. 165(C), pages 456-471.
    17. repec:eee:ecolet:v:162:y:2018:i:c:p:37-40 is not listed on IDEAS
    18. repec:eee:mateco:v:75:y:2018:i:c:p:57-66 is not listed on IDEAS
    19. Shao, Ran & Zhou, Lin, 2016. "Optimal allocation of an indivisible good," Games and Economic Behavior, Elsevier, vol. 100(C), pages 95-112.
    20. Kushnir, Alexey, 2015. "On sufficiency of dominant strategy implementation in environments with correlated types," Economics Letters, Elsevier, vol. 133(C), pages 4-6.
    21. Daske, Thomas, 2017. "Externality Assessments, Welfare Judgments, and Mechanism Design," EconStor Preprints 172494, ZBW - German National Library of Economics.
    22. Hernando-Veciana, Angel & Michelucci, Fabio, 2018. "Inefficient rushes in auctions," Theoretical Economics, Econometric Society, vol. 13(1), January.
    23. repec:spr:reecde:v:21:y:2017:i:2:d:10.1007_s10058-017-0201-0 is not listed on IDEAS
    24. Alexey Kushnir & Shuo Liu, 2017. "On linear transformations of intersections," ECON - Working Papers 255, Department of Economics - University of Zurich.

    More about this item

    Keywords

    Mechanism design; Bayesian implementation; dominant strategy implementation; full surplus extraction; correlation;

    JEL classification:

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

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