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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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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Hagiwara, Makoto, 2019. "Double implementation without no-veto-power," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 124-130.
    5. 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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