Matching for teams |
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Authors: | G Carlier I Ekeland |
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Institution: | 1. Université Paris 9 Dauphine, CEREMADE, Paris Cedex 16, France 2. Canada Research Chair in Mathematical Economics, Department of Mathematics, University of British Columbia, Vancouver, Canada
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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). |
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Keywords: | |
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