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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The authors are grateful to Robert J. McCann for suggesting to them the linear programming formulation of Sect. 6. The first author gratefully acknowledges the support of the ANR, project “Croyances” and of the Fondation du Risque, Chaire Groupama, “Les particuliers face au risque”.
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Carlier, G., Ekeland, I. Matching for teams. Econ Theory 42, 397–418 (2010). https://doi.org/10.1007/s00199-008-0415-z
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DOI: https://doi.org/10.1007/s00199-008-0415-z