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Partially-honest Nash implementation: a full characterization

Author

Listed:
  • Michele Lombardi

    (University of Glasgow
    University of Naples Federico II)

  • Naoki Yoshihara

    (University of Massachusetts Amherst
    Hitotsubashi University
    Kochi University of Technology)

Abstract

A partially-honest individual is a person who follows the maxim, “Do not lie if you do not have to”, to serve your material interest. By assuming that the mechanism designer knows that there is at least one partially-honest individual in a society of $$ n\ge 3$$ n ≥ 3 individuals, a social choice rule that can be Nash implemented is termed partially-honestly Nash implementable. The paper offers a complete characterization of the (unanimous) social choice rules that are partially-honestly Nash implementable. When all individuals are partially-honest, then any (unanimous) rule is partially-honestly Nash implementable. An account of the welfare implications of partially-honest Nash implementation is provided in a variety of environments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:70:y:2020:i:3:d:10.1007_s00199-019-01233-4
    DOI: 10.1007/s00199-019-01233-4
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Núñez, Matías & Laslier, Jean-François, 2015. "Bargaining through Approval," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 63-73.
    2. Guo, Huiyi & Yannelis, Nicholas C., 2022. "Robust coalitional implementation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 553-575.
    3. Lombardi, M. & Yoshihara, N., 2018. "Treading a fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Games and Economic Behavior, Elsevier, vol. 111(C), pages 203-216.
    4. Lombardi, Michele & Yoshihara, Naoki, 2013. "Natural implementation with partially honest agents in economic environments," MPRA Paper 48294, University Library of Munich, Germany.
    5. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    6. Diss, Mostapha & Doghmi, Ahmed & Tlidi, Abdelmonaim, 2015. "Strategy proofness and unanimity in private good economies with single-peaked preferences," MPRA Paper 75469, University Library of Munich, Germany, revised 06 Dec 2016.
    7. 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.
    8. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
    9. Matsushima, Hitoshi, 2022. "Epistemological implementation of social choice functions," Games and Economic Behavior, Elsevier, vol. 136(C), pages 389-402.
    10. Zhiwei Liu & Nicholas C. Yannelis, 2021. "Persuasion in an asymmetric information economy: a justification of Wald’s maxmin preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 801-833, October.
    11. Savva, Foivos, 2021. "Motives and implementation with rights structures," Economics Letters, Elsevier, vol. 204(C).
    12. Hagiwara, Makoto, 2018. "A simple mechanism for double implementation with semi-socially-responsible agents," Economics Letters, Elsevier, vol. 171(C), pages 51-53.
    13. Zhiwei Liu & Nicholas C. Yannelis, 2022. "Mixed strategy implementation under ambiguity," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 167-181, May.
    14. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    15. 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.
    16. Michele Lombardi & Naoki Yoshihara, 2017. "Treading a Â…fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Working Papers SDES-2017-14, Kochi University of Technology, School of Economics and Management, revised Aug 2017.
    17. Savva, Foivos, 2018. "Strong implementation with partially honest individuals," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 27-34.
    18. Altun, Ozan Altuğ & Barlo, Mehmet & Dalkıran, Nuh Aygün, 2023. "Implementation with a sympathizer," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 36-49.
    19. Doghmi, Ahmed, 2011. "A Simple Necessary Condition for Partially Honest Nash Implementation," MPRA Paper 67231, University Library of Munich, Germany, revised 14 Oct 2015.

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    More about this item

    Keywords

    Nash implementation; Pure strategy Nash equilibrium; Partial honesty; Condition $$mu ^{*}$$ μ ∗ (ii);
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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