We develop a network-formation model where the quality of a link depends on the amount invested in it and is determined by a link-formation "technology" , an increasing strictly concave function which is the only exogenous ingredient in the model. The revenue from the investments in links is the information that the nodes receive through the network. Two approaches are considered. First, assuming that the investments in links are made by a planner, the basic question is that of the efficient investments, either relative to a given infrastructure (i.e. a set of feasible links) or in absolute terms. It is proved that efficient networks belong to a special class of weighted nested split graph networks. Second, assuming that links are the result of investments of the node-players involved, there is the question of stability in the underlying network-formation game, be it restricted to a given infrastructure or unrestricted. Necessary and sufficient conditions for stability of the complete and star networks, and nested split graph networks in general, are obtained.

This research is supported by the Spanish Ministerio de Economía y Competitividad under projects ECO2015-66027-P and ECO2015-67519-P (MINECO/FEDER). Both authors also bene t from the Basque Government Departa-mento de Educación, Política Lingüística y Cultura funding for Grupos Consolidados IT869-13 and IT568-13.