Matching for teams

Abstract

We are given a list of tasks Z and a population divided into several groups Xj of equal size. Performing one task z requires constituting a team with exactly one member xj from every group. There is a cost (or reward) for participation: if type xj chooses task z, he receives pj (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). © 2008 Springer-Verlag.