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Implementation, Honesty, and Common Knowledge

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  • Hitoshi Matsushima

    (University of Tokyo)

Abstract

We investigate the unique implementation problem of social choice functions (SCFs) from ethical and epistemological concerns. According to Matsushima and Noda (2020), we consider the possibility that in higher-order beliefs there exists an agent who is honest, that is, motivated by intrinsic preference for honesty as well as material interest. We assume only weak honesty in that an honest agent is mostly motivated by material interests and even tells a white lie. We show a very permissive result that any social choice function is uniquely implementable in Bayes Nash equilibrium if “all agents are selfish†never happens to be common knowledge. Hence, any SCF is uniquely implementable even if all agents are selfish and "all agents are selfish" is mutual knowledge. Importantly, any ethical SCF is uniquely implementable whenever "all agents are selfish" never happens to be common knowledge while it is never uniquely implementable otherwise.

Suggested Citation

  • Hitoshi Matsushima, 2020. "Implementation, Honesty, and Common Knowledge," CARF F-Series CARF-F-500, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf500
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    References listed on IDEAS

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    6. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, vol. 139(1), pages 353-359, March.
    7. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
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    10. Savva, Foivos, 2018. "Strong implementation with partially honest individuals," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 27-34.
    11. Matsushima, Hitoshi, 2008. "Behavioral aspects of implementation theory," Economics Letters, Elsevier, vol. 100(1), pages 161-164, July.
    12. Johannes Abeler & Daniele Nosenzo & Collin Raymond, 2019. "Preferences for Truth‐Telling," Econometrica, Econometric Society, vol. 87(4), pages 1115-1153, July.
    13. Ortner, Juan, 2015. "Direct implementation with minimally honest individuals," Games and Economic Behavior, Elsevier, vol. 90(C), pages 1-16.
    14. Mukherjee, Saptarshi & Muto, Nozomu & Ramaekers, Eve, 2017. "Implementation in undominated strategies with partially honest agents," Games and Economic Behavior, Elsevier, vol. 104(C), pages 613-631.
    15. 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.
    16. Hitoshi Matsushima, 2013. "Process manipulation in unique implementation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 883-893, October.
    17. Michele Lombardi & Naoki Yoshihara, 2017. "Natural implementation with semi-responsible agents in pure exchange economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1015-1036, November.
    18. 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.
    19. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
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    21. 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.
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    23. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    Cited by:

    1. Matsushima, Hitoshi, 2022. "Epistemological implementation of social choice functions," Games and Economic Behavior, Elsevier, vol. 136(C), pages 389-402.
    2. Hitoshi Matsushima & Shunya Noda, 2020. "Epistemological Mechanism Design (Revised version of CARF-F-496)," CARF F-Series CARF-F-498, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Feb 2021.
    3. Savva, Foivos, 2021. "Motives and implementation with rights structures," Economics Letters, Elsevier, vol. 204(C).

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