Free intermediation in resource transmission

We provide a framework for the study of the allocation of a divisible resource from a planner to agents via intermediaries. Intermediaries simultaneously post fees for their services, and the planner optimally selects a subset of them to assist in the transmission of the resource. We provide necessary and sufficient conditions for the existence of a perfectly competitive equilibrium in which intermediaries selected by the planner collect no fees. Furthermore, these conditions are necessary and sufficient for the uniqueness of an equilibrium with the property that intermediaries not selected by the planner post zero prices. Furthermore, these conditions are necessary and sufficient to guarantee the uniqueness of equilibrium when intermediaries who are not selected post fees equal to zero.