A connections model with decreasing returns link-formation technology

We study a connections model where the strength of a link depends on the amount invested in it and is determined by an increasing strictly concave function. The revenue from investments in links is the information that the nodes receive through the network. First, the structures of efficient networks are characterized, and conditions for optimal investments constrained to supporting a given network are obtained. Second, assuming that links are the result of investments by the node-players involved, there is the question of stability. We introduce and characterize a notion of marginal equilibrium weaker than that of Nash equilibrium, and identify different marginally stable structures. Efficiency and stability are shown to be incompatible, but partial subsidizing is shown to be able to bridge the gap.