Efficient Networks in Connections Models with Heterogeneous Nodes and Links

We complete the extension of the results on efficiency in the seminal connections model of Jackson and Wolinsky (1996), partially addressed in previous papers. In a model where both nodes and links are heterogeneous, we prove that efficiency is reached by networks with a unique non-trivial component, within which one of the nodes with the highest value is directly connected with the others in the component, among which some pairs are directly connected. Moreover, the greater the sum of the values of two nodes, the greater the strength of their connection, be it direct by a link or indirect by means of two links through the central node. Nash stability and a suitable notion of pairwise stability are shown to be incompatible with efficiency