Communication networks with endogenous link strength

This paper analyzes the formation of communication networks when players choose endogenously their investment on communication links. We consider two alternative definitions of network reliability; product reliability, where the decay of information depends on the product of the strength of communication links, and min reliability where the speed of connection is affected by the weakest communication link. When investments are separable, the architecture of the efficient network depends crucially on the shape of the transformation function linking investments to the quality of communication links. With increasing marginal returns to investment, the efficient network is a star ; with decreasing marginal returns, the conflict between maximization of direct and indirect benefits prevents a complete characterization of efficient networks. However, with min reliability, the efficient network must be a tree. Furthermore, in the particular case of linear transformation functions, in an efficient network, all links must have equal strength. When investments are perfect complements, the results change drastically: under product reliability, the efficient net- work must contain a cycle, and is in fact a circle for small societies. With min reliability, the efficient network is either a circle or a line. As in classical models of network formation, efficient networks may not be supported by private investment decisions. We provide examples to show that the star may not be stable when the transformation functions is strictly convex. We also note that with perfect substitutes and perfect complements (when the efficient network displays a very symmetric structure), the efficient network can indeed be supported by private investments when the society is large.