Duality and Existence for a Class of Mass Transportation Problems and Economic Applications

Abstract

We establish duality, existence and uniqueness results for a class of mass transportations problems. We extend a technique of W. Gangbo 9] using the Euler Equation of the dual problem. This is done by introducing the h-Fenchel Transform and using its basic properties. The cost functions we consider satisfy a generalization of the so-called Spence-Mirrlees condition which is well-known by economists in dimension 1. We therefore end this article by a somehow unexpected application to the economic theory of incentives. R esum e Nous etablissons dans cet article des r esultats de dualit e, d'existence et d'uni-cit e pour une classe de probl emes de transport optimal de masse. La nou-veaut e r eside ici dans l'emploi de la transform ee de Fenchel h-convexe qui per-met d'utiliser un argument de W. Gangbo 9] consistant a exploiter l' equation d'Euler du probl eme dual. Les co^ uts de transport que nous consid erons satis-font une condition g en eralisant la condition de Spence-Mirrlees bien connue des economistes en dimension 1. Nous terminons ainsi cet article par une application de notre r esultat a la th eorie economique des incitations.

Cite this paper

@inproceedings{Carlier2000DualityAE, title={Duality and Existence for a Class of Mass Transportation Problems and Economic Applications}, author={Guillaume Carlier}, year={2000} }