A solution to the two-person implementation problem

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

1 PSE - Paris School of Economics
2 PJSE - Paris Jourdan Sciences Economiques
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 strike mechanisms as a solution to the classical problem of Hurwicz and Schmeidler [1978] and Maskin [1999] according to which, in twoperson societies, no Pareto efficient rule is Nash-implementable. A strike mechanism specifies the number of alternatives that each player vetoes. Each player simultaneously casts these vetoes and the mechanism selects randomly one alternative among the unvetoed ones. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, these mechanisms are deterministic-in-equilibrium. They 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 Nash-implementable rule is a Pareto-and-veto rule and hence is implementable through a strike mechanism.

Keywords: Nash implementation; Two players; Pareto efficiency

Domains: Economics and Finance

Jean-François Laslier, Matias Nunez, M Remzi Sanver. A solution to the two-person implementation problem. 2020. ⟨halshs-02173504v3⟩