On the Interaction between Heterogeneity and Decay in Directed Networks

In this paper, we examine the role played by heterogeneity in the connection model. In sharp contrast to the homogeneous cases we show that under heterogeneity involving only two degrees of freedom, all networks can be supported as Nash or efficient. Moreover, we show that there does not always exist Nash networks. However, we show that on reducing heterogeneity, both the earlier “anything goes” result and the non existence problem disappear.