Heterogeneity and Link Imperfections in Nash Networks

Heterogeneity in Nash networks with two-way flow can arise due to differences in the follow- ing four variables: (i) the value of information held by players, (ii) the rate at which information decays as it traverses the network, (iii) the probability with which a link transmits information, and (iv) the cost of forming a link. Observe that the second and third forms of heterogeneity are also instances of link imperfections. In sharp contrast to the homogeneous cases in this paper we show that for any type of link imperfection, under heterogeneity involving only two degrees of freedom, all networks can be supported as Nash or efficient. To address the question of conflict between stability and efficiency, we then identify conditions under which efficient networks are also Nash. We also find that cost heterogeneity leads to non-existence of Nash networks in models with and without link imperfections. We show that in general there is no relationship between the decay and probabilistic models of network formation. Finally, we show that on reducing heterogeneity the earlier �anything goes� result disappears.