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Robust virtual implementation

Author

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  • Bergemann, Dirk

    () (Department of Economics, Yale University)

  • Morris, Stephen

    () (Department of Economics, Princeton University)

Abstract

In a general interdependent preference environment, we characterize when two payoff types can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two payoff types are strategically distinguishable if and only if they satisfy a separability condition. The separability condition for each agent essentially requires that there is not too much interdependence in preferences across agents. A social choice function, mapping payoff type profiles to outcomes, can be robustly virtually implemented if there exists a mechanism such that every equilibrium on every type space achieves an outcome that is arbitrarily close to the outcome generated by the social choice function. This definition is equivalent to requiring virtual implementation in iterated deletion of strategies that are strictly dominated for all beliefs. The social choice function is robustly measurable if strategically indistinguishable payoff types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation.

Suggested Citation

  • Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
  • Handle: RePEc:the:publsh:453
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    3. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.
    4. Hitoshi Matsushima, 2017. "Dynamic Implementation, Verification, and Detection," CARF F-Series CARF-F-416, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
    6. Ghossoub, Mario, 2010. "Belief heterogeneity in the Arrow-Borch-Raviv insurance model," MPRA Paper 37630, University Library of Munich, Germany, revised 22 Mar 2012.
    7. 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.
    8. Di Tillio, Alfredo, 2011. "A robustness result for rationalizable implementation," Games and Economic Behavior, Elsevier, vol. 72(1), pages 301-305, May.
    9. Hitoshi Matsushima, 2015. "Implementation, Verification, and Detection," CIRJE F-Series CIRJE-F-991, CIRJE, Faculty of Economics, University of Tokyo.
    10. Penta, Antonio, 2015. "Robust dynamic implementation," Journal of Economic Theory, Elsevier, vol. 160(C), pages 280-316.
    11. Adachi, Tsuyoshi, 2014. "Robust and secure implementation: equivalence theorems," Games and Economic Behavior, Elsevier, vol. 86(C), pages 96-101.
    12. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    13. Gul, Faruk & Pesendorfer, Wolfgang, 2016. "Interdependent preference models as a theory of intentions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 179-208.
    14. 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.
    15. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.

    More about this item

    Keywords

    Mechanism design; virtual implementation; robust implementation; rationalizability; ex-post incentive compatibility;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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