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Nash Implementation in an Allocation Problem with Single-Dipped Preferences

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  • Ahmed Doghmi

    (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)

Abstract

In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic ( but they do not satisfy no-veto power) and hence Nash implementable.

Suggested Citation

  • Ahmed Doghmi, 2013. "Nash Implementation in an Allocation Problem with Single-Dipped Preferences," Games, MDPI, vol. 4(1), pages 1-12, January.
    • Handle: RePEc:gam:jgames:v:4:y:2013:i:1:p:38-49:d:23225
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    References listed on IDEAS

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    2. Dutta, Bhaskar & Sen, Arunava, 2012. "Nash implementation with partially honest individuals," Games and Economic Behavior, Elsevier, vol. 74(1), pages 154-169.
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    11. 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.
    12. 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.
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    16. Ahmed Doghmi & Abderrahmane ZIAD, 2012. "On Partial Honesty Nash Implementation," Economics Working Paper Archive (University of Rennes & University of Caen) 201201, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    17. Doghmi, Ahmed & Ziad, Abderrahmane, 2008. "Nash implementation in exchange economies with single-peaked preferences," Economics Letters, Elsevier, vol. 100(1), pages 157-160, July.
    18. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, September.
    19. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
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    21. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Yamamura, Hirofumi, 2023. "Uniform rules for the allocation problem with single-dipped preferences when free-disposal is possible," Economics Letters, Elsevier, vol. 230(C).
    4. Dietzenbacher, Bas & Tamura, Yuki, 2023. "Stable and efficient reallocations when preferences are single-dipped," Economics Letters, Elsevier, vol. 231(C).
    5. Doğan, Battal, 2016. "Nash-implementation of the no-envy solution on symmetric domains of economies," Games and Economic Behavior, Elsevier, vol. 98(C), pages 165-171.
    6. Dietzenbacher, Bas & Tamura, Yuki, 2023. "Fair and efficient allocations when preferences are single-dipped," Research Memorandum 009, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Doghmi, Ahmed, 2011. "A Simple Necessary Condition for Partially Honest Nash Implementation," MPRA Paper 67231, University Library of Munich, Germany, revised 14 Oct 2015.
    8. 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.
    9. 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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