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Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine

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  • Artemov, Georgy
  • Kunimoto, Takashi
  • Serrano, Roberto

Abstract

We study a mechanism design problem where arbitrary restrictions are placed on the sets of first-order beliefs of agents. Calling these restrictions Δ, we use Δ-rationalizability (Battigalli and Siniscalchi, 2003, [5]) as our solution concept, and require that a mechanism virtually implement a socially desirable outcome. We obtain two necessary conditions, Δ-incentive compatibility and Δ-measurability and show that the latter is satisfied as long as a particular zero-measure set of first-order beliefs is ruled out. In environments allowing small transfers of utility among agents, these two conditions are also sufficient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:424-447
    DOI: 10.1016/j.jet.2012.12.015
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    References listed on IDEAS

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    1. Neeman, Zvika, 2004. "The relevance of private information in mechanism design," Journal of Economic Theory, Elsevier, vol. 117(1), pages 55-77, July.
    2. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    3. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    4. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    5. Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
    6. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
    7. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    8. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, January.
    9. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    10. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    11. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    12. 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.
    13. Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
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    Citations

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    Cited by:

    1. Pierpaolo Battigalli & Gabriele Beneduci & Pietro Tebaldi, 2017. "Interactive Epistemology in Simple Dynamic Games with a Continuum of Strategies," Working Papers 602, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. repec:eee:gamebe:v:113:y:2019:i:c:p:285-305 is not listed on IDEAS
    3. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.
    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. Núñez, Matías & Pivato, Marcus, 2019. "Truth-revealing voting rules for large populations," Games and Economic Behavior, Elsevier, vol. 113(C), pages 285-305.
    6. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei, 2015. "Implementation with Transfers," Discussion Papers 2015-04, Graduate School of Economics, Hitotsubashi University.
    7. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    8. Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2014. "Mechanism Design with Bounded Depth of Reasoning and Small Modeling Mistakes," Working Papers 2014-7, Brown University, Department of Economics.
    9. Oury, Marion, 2015. "Continuous implementation with local payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 656-677.

    More about this item

    Keywords

    Wilson doctrine; Mechanism design; Robust virtual implementation; Δ-rationalizability; Incentive compatibility; Measurability; Type diversity;

    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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