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Nash implementation in private good economies with single-plateaued preferences and in matching problems

Author

Listed:
  • Ahmed Doghmi

    (QSM Laboratory - Mohammadia School of Engineering - 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 paper we explore the problem of Nash implementation providing two new properties called I-monotonicity and I-weak no-veto power. These properties form together with unanimity a new sufficient condition for a social choice correspondence to be implementable in Nash equilibria with at least three agents. As applications, we prove that: (1) In private good economies with single-plateaued preferences, each solution of the problem of fair division that has a full range is Nash implementable if and only if it satisfies Maskin monotonicity, (2) In matching problems, Maskin monotonicity is a necessary and sufficient condition for implementation.

Suggested Citation

  • Ahmed Doghmi & Abderrahmane Ziad, 2015. "Nash implementation in private good economies with single-plateaued preferences and in matching problems," Post-Print halshs-01116843, HAL.
    • Handle: RePEc:hal:journl:halshs-01116843
    DOI: 10.1016/j.mathsocsci.2014.11.002
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    Cited by:

    1. Dolors Berga, 2025. "A note on strategy-proofness and single-plateaued preferences," Economics Bulletin, AccessEcon, vol. 45(4), pages 1666-1671.
    2. 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.
    3. Diss, Mostapha & Doghmi, Ahmed & Tlidi, Abdelmonaim, 2016. "Strategy proofness and unanimity in many-to-one matching markets," MPRA Paper 75927, University Library of Munich, Germany, revised 08 Dec 2016.
    4. 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.
    5. Michele Lombardi & Foivos Savva & Nikolas Zivanas, 2023. "Implementation in strong core by codes of rights," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(3), pages 503-515, April.
    6. Hagiwara, Makoto, 2019. "Double implementation without no-veto-power," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 124-130.

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