0, there exists a mechanism such that for each preference profile t, its set of Nash equilibrium outcomes at t is E-closed to the socially desirable set F(t). Under a domain restriction, we obtain the following result: When there are at least three agents, any F is virtually implementable in Nash equilibrium, as well as in rationalizable strategies, by a bounded mechanism. No "tail-chasing" constructions, common in the constructive proofs of the literature, is used to assure that undesired strategy combinations do not form a Nash equilibrium."> 0, there exists a mechanism such that for each preference profile t, its set of Nash equilibrium outcomes at t is E-closed to the socially desirable set F(t). Under a domain restriction, we obtain the following result: When there are at least three agents, any F is virtually implementable in Nash equilibrium, as well as in rationalizable strategies, by a bounded mechanism. No "tail-chasing" constructions, common in the constructive proofs of the literature, is used to assure that undesired strategy combinations do not form a Nash equilibrium."> 0, there">
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Virtual implementation by bounded mechanisms: Complete information

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Abstract
A social choice rule (SCR) F maps preference profiles to lotteries over some finite set of outcomes. F is virtually implementable in (pure and mixed) Nash equilibria provided that for all E > 0, there exists a mechanism such that for each preference profile t, its set of Nash equilibrium outcomes at t is E-closed to the socially desirable set F(t). Under a domain restriction, we obtain the following result: When there are at least three agents, any F is virtually implementable in Nash equilibrium, as well as in rationalizable strategies, by a bounded mechanism. No "tail-chasing" constructions, common in the constructive proofs of the literature, is used to assure that undesired strategy combinations do not form a Nash equilibrium.

Suggested Citation

  • Ritesh Jain & Michele Lombardi, 2019. "Virtual implementation by bounded mechanisms: Complete information," IEAS Working Paper : academic research 19-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:19-a001
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    File URL: https://www.econ.sinica.edu.tw/~econ/pdfPaper/19-A001(all).pdf
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    References listed on IDEAS

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    1. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404, World Scientific Publishing Co. Pte. Ltd..
    2. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    3. Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2019. "Level-$k$ Mechanism Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1207-1227.
    4. Vincent P. Crawford, 1977. "A Game of Fair Division," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(2), pages 235-247.
    5. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    6. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    7. repec:hal:pseose:halshs-00943301 is not listed on IDEAS
    8. Takashi Kunimoto & Roberto Serrano, 2016. "Rationalizable Implementation of Correspondences," Working Papers 2016-4, Brown University, Department of Economics.
    9. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    10. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    11. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    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. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    14. Hitoshi Matsushima, 2019. "Implementation without expected utility: ex-post verifiability," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(4), pages 575-585, December.
    15. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    16. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
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    Cited by:

    1. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.

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    More about this item

    Keywords

    : Virtual implementation; pure and mixed Nash equilibria; rationalizability; social choice rules;
    All these keywords.

    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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