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Economic Theory

, Volume 42, Issue 2, pp 397–418 | Cite as

Matching for teams

  • G. Carlier
  • I. Ekeland
Symposium

Abstract

We are given a list of tasks Z and a population divided into several groups X j of equal size. Performing one task z requires constituting a team with exactly one member x j from every group. There is a cost (or reward) for participation: if type x j chooses task z, he receives p j (z); utilities are quasi-linear. One seeks an equilibrium price, that is, a price system that distributes all the agents into distinct teams. We prove existence of equilibria and fully characterize them as solutions to some convex optimization problems. The main mathematical tools are convex duality and mass transportation theory. Uniqueness and purity of equilibria are discussed. We will also give an alternative linear-programming formulation as in the recent work of Chiappori et al. (Econ Theory, to appear).

Keywords

Matching Equilibria Convex duality Optimal transportation 

JEL Classification

C62 C78 

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References

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  4. Ekeland I.: An optimal matching problem. ESAIM Contrôle Optimal et Calcul des Variations 11(1), 57–71 (2005)CrossRefGoogle Scholar
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Université Paris 9 Dauphine, CEREMADEParis Cedex 16France
  2. 2.Canada Research Chair in Mathematical Economics, Department of MathematicsUniversity of British ColumbiaVancouverCanada

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