A solution to the two-person implementation problem

Jean-François Laslier (1, 2) , Matias Nunez (3, 4) , M Remzi Sanver (5)

1 PJSE - Paris Jourdan Sciences Economiques
2 PSE - Paris School of Economics
3 CECO - Laboratoire d'économétrie de l'École polytechnique
4 CREST - Centre de Recherche en Economie et Statistique [Bruz]
5 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We propose a solution to the classical problem of Hurwicz and Schmeidler [1978] and Maskin [1999] according to which, in two-person societies, no Pareto efficient rule is Nash-implementable. To this end, we consider implementation through mechanisms that are deterministic-in-equilibrium while lotteries are allowed off-equilibrium. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, we build simple veto mechanisms that Nash implement a class of Pareto efficient social choice rules called Pareto-and-veto rules. Moreover, under mild richness conditions on the domain of preferences over lotteries, any Pareto efficient Nashimplementable rule is a Pareto-and-veto rule and hence is implementable through one of our simple veto mechanisms.

Domains: Economics and Finance

Jean-François Laslier, Matias Nunez, M Remzi Sanver. A solution to the two-person implementation problem. 2019. ⟨halshs-02173504v2⟩