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A Characterization of Virtual Bayesian Implementation

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  • Roberto Serrano

    (Department of Economics, Brown University)

  • Rajiv Vohra

    (Department of Economics, Brown University)

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).

Suggested Citation

  • Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science.
    • Handle: RePEc:ads:wpaper:0028
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    References listed on IDEAS

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    16. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-792, May.
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    Citations

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
    2. Hitoshi Matsushima, 2005. "On Detail‐Free Mechanism Design And Rationality," The Japanese Economic Review, Japanese Economic Association, vol. 56(1), pages 41-54, March.
    3. 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.
    4. 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.
    5. 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.
    6. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    7. Núñez, Matías & Pivato, Marcus, 2019. "Truth-revealing voting rules for large populations," Games and Economic Behavior, Elsevier, vol. 113(C), pages 285-305.
    8. Gerardi, Dino & McLean, Richard & Postlewaite, Andrew, 2009. "Aggregation of expert opinions," Games and Economic Behavior, Elsevier, vol. 65(2), pages 339-371, March.
    9. 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.
    10. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
    11. 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..
    12. Kobbi Nissim & Rann Smorodinsky & Moshe Tennenholtz, 2018. "Segmentation, Incentives, and Privacy," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1252-1268, November.
    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. 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.
    15. Chen, Yi-Chun & Kunimoto, Takashi & 国本, 隆 & Sun, Yifei, 2015. "Implementation with Transfers," Discussion Papers 2015-04, Graduate School of Economics, Hitotsubashi University.
    16. Peralta, Esteban, 2019. "Bayesian implementation with verifiable information," Games and Economic Behavior, Elsevier, vol. 116(C), pages 65-72.
    17. Takashi Kunimoto & Rene Saran & Roberto Serrano, 2020. "Interim Rationalizable Implementation of Functions," Working Papers 2020-23, Brown University, Department of Economics.
    18. 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.

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    More about this item

    Keywords

    Virtual monotonicity; Bayesian monotonicity; Maskin monotonicity; virtual Bayesian implementation; incentive compatibility; type diversity; decentralization; incomplete information;
    All these keywords.

    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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