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

Ahmed Doghmi (1) , Abderrahmane Ziad (2)

1 QSM Laboratory - Mohammadia School of Engineering
2 CREM - Centre de recherche en économie et management

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.

Mots clés: Nash implementation; private good economies with single-plateaued preferences; matching problems

Domaines: Economies et finances

Ahmed Doghmi, Abderrahmane Ziad. Nash implementation in private good economies with single-plateaued preferences and in matching problems. Mathematical Social Sciences, 2015, 73, pp.32-39. ⟨10.1016/j.mathsocsci.2014.11.002⟩. ⟨halshs-01116843⟩