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On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition

Author

Listed:
  • Ahmed Doghmi

    (International University of Rabat)

  • Abderrahmane Ziad

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract
In this article, we study the problem of Nash implementation in private good economies with single-peaked, single-plateaued, and single-dipped preferences in the presence of at least one minimally honest agent. We prove that all solutions of the problem of fair division satisfying unanimity can be implemented in Nash equilibria as long as there are at least three agents participating in the mechanism (game form). To justify this result, we provide a list of solutions which violate the condition of no-veto power.

Suggested Citation

  • Ahmed Doghmi & Abderrahmane Ziad, 2013. "On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition," Post-Print halshs-00869873, HAL.
    • Handle: RePEc:hal:journl:halshs-00869873
    DOI: 10.1515/bejte-2012-0028
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    References listed on IDEAS

    as
    1. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 1-15, March.
    2. Lombardi, Michele & Yoshihara, Naoki, 2012. "Natural Implementation with Partially Honest Agents," Discussion Paper Series 561, Institute of Economic Research, Hitotsubashi University.
    3. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Reexamination of Maskin's Theorem on Nash implementability," Economics Letters, Elsevier, vol. 100(1), pages 150-152, July.
    4. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    5. Lombardi, Michele & Yoshihara, Naoki & 吉原, 直毅, 2011. "Partially-honest Nash implementation: Characterization results," CCES Discussion Paper Series 43, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    6. Ville Korpela, 2014. "Bayesian implementation with partially honest individuals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 647-658, October.
    7. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    8. Doghmi Ahmed, 2013. "Nash Implementation in Private Good Economies when Preferences are Single-Dipped with Best Indifferent Allocations," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 35-42, October.
    9. Ahmed Doghmi & Abderrahmane Ziad, 2013. "Nash Implementation in Private Good Economies with Single-Plateaued Preferences," Economics Working Paper Archive (University of Rennes & University of Caen) 201311, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Doghmi Ahmed, 2013. "Nash Implementation in Private Good Economies when Preferences are Single-Dipped with Best Indifferent Allocations," Mathematical Economics Letters, De Gruyter, vol. 1(1), pages 35-42, October.
    2. Doghmi, Ahmed & Ziad, Abderrahmane, 2015. "Nash implementation in private good economies with single-plateaued preferences and in matching problems," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 32-39.
    3. Ahmed Doghmi & Abderrahmane Ziad, 2013. "Nash Implementation in Private Good Economies with Single-Plateaued Preferences," Economics Working Paper Archive (University of Rennes & University of Caen) 201311, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    4. Fumiya Inoue & Hirofumi Yamamura, 2023. "Binary mechanism for the allocation problem with single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 647-669, May.
    5. 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.
    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. Ville Korpela, 2014. "Bayesian implementation with partially honest individuals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 647-658, October.
    8. Ville Korpela, 2017. "All Deceptions Are Not Alike: Bayesian Mechanism Design with a Social Norm against Lying," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 173(2), pages 376-393, June.
    9. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    10. Savva, Foivos, 2018. "Strong implementation with partially honest individuals," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 27-34.
    11. Hagiwara, Makoto, 2019. "Double implementation without no-veto-power," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 124-130.
    12. Doghmi, Ahmed, 2011. "A Simple Necessary Condition for Partially Honest Nash Implementation," MPRA Paper 67231, University Library of Munich, Germany, revised 14 Oct 2015.
    13. Doghmi Ahmed, 2014. "Nash Implementation in Rationing Problems with Single-Crossing Preferences," Mathematical Economics Letters, De Gruyter, vol. 1(2-4), pages 69-74, July.
    14. Doghmi Ahmed, 2016. "On Nash Implementability in Allotment Economies under Domain Restrictions with Indifference," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 16(2), pages 767-795, June.

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    More about this item

    Keywords

    Nash implementation; partial honesty; single-peaked preferences; single-plateaued preferences; single-dipped preferences;
    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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