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A Characterization of Virtual Bayesian Implementation

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Abstract

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity - known to be necessary for Bayesian implementation. Virtual monotonicity is weak in the sense that it is generically satisfied in environments with at least three alternatives. This implies that in most environments virtual Bayesian implementation is as successful as it can be (incentive compatibility is the only condition needed).
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Suggested Citation

  • Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Working Papers 2002-11, Brown University, Department of Economics.
    • Handle: RePEc:bro:econwp:2002-11
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    Cited by:

    1. Hitoshi Matsushima, 2005. "On Detail‐Free Mechanism Design And Rationality," The Japanese Economic Review, Japanese Economic Association, vol. 56(1), pages 41-54, March.
    2. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics.
    3. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    4. Núñez, Matías & Pivato, Marcus, 2019. "Truth-revealing voting rules for large populations," Games and Economic Behavior, Elsevier, vol. 113(C), pages 285-305.
    5. Gerardi, Dino & McLean, Richard & Postlewaite, Andrew, 2009. "Aggregation of expert opinions," Games and Economic Behavior, Elsevier, vol. 65(2), pages 339-371, March.
    6. Marcus Pivato, 2016. "Statistical Utilitarianism," Studies in Political Economy, in: Maria Gallego & Norman Schofield (ed.), The Political Economy of Social Choices, pages 187-204, Springer.
    7. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    8. Chen, Yi-Chun & Kunimoto, Takashi & 国本, 隆 & Sun, Yifei, 2015. "Implementation with Transfers," Discussion Papers 2015-04, Graduate School of Economics, Hitotsubashi University.
    9. Peralta, Esteban, 2019. "Bayesian implementation with verifiable information," Games and Economic Behavior, Elsevier, vol. 116(C), pages 65-72.
    10. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    11. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    12. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers 1519, Cowles Foundation for Research in Economics, Yale University.
    13. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
    14. Marcus Pivato, 2016. "Asymptotic utilitarianism in scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 431-458, August.
    15. Kobbi Nissim & Rann Smorodinsky & Moshe Tennenholtz, 2018. "Segmentation, Incentives, and Privacy," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1252-1268, November.
    16. Antonio Cabrales & Roberto Serrano, 2012. "Stochastically stable implementation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 59-72, March.
    17. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    18. Takashi Kunimoto & Rene Saran & Roberto Serrano, 2020. "Interim Rationalizable Implementation of Functions," Economics and Statistics Working Papers 21-2020, Singapore Management University, School of Economics.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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