Cooperative production and efficiency

We characterize the sharing rule for which a contribution mechanism achieves efficiency in a cooperative production setting when agents are heterogeneous. The sharing rule bears no resemblance to those considered by the previous literature. We also show for a large class of sharing rules that if Nash equilibrium yields efficient allocations, the production function displays constant returns to scale, a case in which cooperation in production is useless. ∗ We thank Juan Enrique Martinez-Legaz, Hervé Moulin and Joaquim Silvestre for helpful comments. The first author acknowledges financial support from SEJ2005-01481/ECON and FEDER, 2005SGR-00454, and the Barcelona Economics Program, CREA. The second author acknowledges financial support from SEJ200506167/ECON.