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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

    as
    1. 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.
    2. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    3. 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.
    4. Johannes Abeler & Daniele Nosenzo & Collin Raymond, 2019. "Preferences for Truth‐Telling," Econometrica, Econometric Society, vol. 87(4), pages 1115-1153, July.
    5. Sebastian Morris, 2022. "Introduction," India Studies in Business and Economics, in: Macroeconomic Policy in India Since the Global Financial Crisis, chapter 0, pages 1-21, Springer.
    6. 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.
    7. 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.
    8. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    9. 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..
    10. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    11. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
    12. Yadav, Sonal, 2016. "Selecting winners with partially honest jurors," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 35-43.
    13. 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.
    14. Matsushima, Hitoshi, 2008. "Role of honesty in full implementation," Journal of Economic Theory, Elsevier, vol. 139(1), pages 353-359, March.
    15. 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.
    16. Ortner, Juan, 2015. "Direct implementation with minimally honest individuals," Games and Economic Behavior, Elsevier, vol. 90(C), pages 1-16.
    17. repec:hal:pseose:halshs-00943301 is not listed on IDEAS
    18. Saporiti, Alejandro, 2014. "Securely implementable social choice rules with partially honest agents," Journal of Economic Theory, Elsevier, vol. 154(C), pages 216-228.
    19. Matsushima, Hitoshi, 2008. "Behavioral aspects of implementation theory," Economics Letters, Elsevier, vol. 100(1), pages 161-164, July.
    20. Doğan, Battal, 2017. "Eliciting the socially optimal allocation from responsible agents," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 103-110.
    21. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    22. Savva, Foivos, 2018. "Strong implementation with partially honest individuals," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 27-34.
    23. Bergemann & Morris, . "An Introduction to Robust Mechanism Design," Foundations and Trends(R) in Microeconomics, now publishers, vol. 8(3), pages 169-230.
    24. 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.
    25. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    26. 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. 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.
    2. Matsushima, Hitoshi, 2022. "Epistemological implementation of social choice functions," Games and Economic Behavior, Elsevier, vol. 136(C), pages 389-402.
    3. Savva, Foivos, 2021. "Motives and implementation with rights structures," Economics Letters, Elsevier, vol. 204(C).

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