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

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  • Doghmi Ahmed

    (Department of Economics and Finance, National Institute of Statistics and Applied Economics, Madinat Al Irfane, Rabat Institutes, 10100 Rabat, Morocco; University of Caen, Center for Research in Economics and Management (UMR CNRS 6211), 19 Rue Claude Bloch 14032 Caen, Cedex, France)

  • Ziad Abderrahmane

    (Department of Economics, University of Caen, Center for Research in Economics and Management (UMR CNRS 6211), 19 Rue Claude Bloch 14032 Caen, Cedex, France)

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

  • Doghmi Ahmed & Ziad Abderrahmane, 2013. "On Partially Honest Nash Implementation in Private Good Economies with Restricted Domains: A Sufficient Condition," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 415-428, September.
    • Handle: RePEc:bpj:bejtec:v:13:y:2013:i:1:p:14:n:14
    DOI: 10.1515/bejte-2012-0028
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    References listed on IDEAS

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    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. 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.
    5. 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.
    6. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    7. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. Savva, Foivos, 2018. "Strong implementation with partially honest individuals," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 27-34.
    3. 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.
    4. 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.
    5. Hagiwara, Makoto, 2019. "Double implementation without no-veto-power," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 124-130.
    6. 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.
    7. Mostapha Diss & Ahmed Doghmi & Abdelmonaim Tlidi, 2015. "Strategy proofness and unanimity in private good economies with single-peaked preferences," Working Papers 1528, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    8. Doghmi, Ahmed, 2011. "A Simple Necessary Condition for Partially Honest Nash Implementation," MPRA Paper 67231, University Library of Munich, Germany, revised 14 Oct 2015.
    9. 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.
    10. 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.
    11. Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    12. 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.
    13. 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.
    14. 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.

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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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