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 de…nitions 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 a¤ected by the weakest communication link. When investments are separable, the architecture of the e¢ cient 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 e¢ cient network is a star ; with decreasing marginal returns, the con‡ict between maximization of direct and indirect bene…ts prevents a complete characterization of e¢ cient networks. However, with min reliability, the e¢ cient network must be a tree. Furthermore, in the particular case of linear transformation functions, in an e¢ cient network, all links must have equal strength. When investments are perfect complements, the results change drastically: under product reliability, the e¢ cient network must contain a cycle, and is in fact a circle for small societies. With min reliability, the e¢ cient network is either a circle or a line. We thank C.Blackorby and M. Jackson for helpful discussions. We have bene…ted from the comments of participants in seminars and conferences at Guanajuato... yBloch is at GREQAM, Universite d’Aix-Marseille, 2 rue de Charite, 13002 Marseille, France. Dutta is in the Department of Economics, University of Warwick, Coventry CV4 7AL, England.