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Duality and existence for a class of mass transportation problems and economic applications

Carlier, Guillaume (2003), Duality and existence for a class of mass transportation problems and economic applications, in Maruyama, T.; Kusuoka, S., Advances in Mathematical Economics, 5, Springer : Berlin, p. 1-21

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Type
Chapitre d'ouvrage
Date
2003
Book title
Advances in Mathematical Economics, 5
Book author
Maruyama, T.; Kusuoka, S.
Publisher
Springer
Published in
Berlin
ISBN
978-4-431-00003-7
Number of pages
200
Pages
1-21
Metadata
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Author(s)
Carlier, Guillaume
Abstract (FR)
Nous établissons dans cet article des résultats de dualité, d’existence et d’unicité pour une classe de problèmes de transport optimal de masse. La nouveauté réside ici dans l’emploi de la transformée de Fenchel h-convexe qui permet d’utiliser un argument de W. Gangbo [9] consistant à exploiter l’équation d’Euler du problème dual. Les coûts de transport que nous considérons satisfont une condition généralisant la condition de Spence-Mirrlees bien connue des économistes en dimension 1. Nous terminons ainsi cet article par une application de notre résultat à la théorie économique des incitations.
Abstract (EN)
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.
Subjects / Keywords
mass transportations problems; economic theory of incentives
JEL
D82 - Asymmetric and Private Information; Mechanism Design
C61 - Optimization Techniques; Programming Models; Dynamic Analysis

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