This paper studies the welfare implications of equilibrium behavior in a market characterized by competition between two interconnected telecommunication firms, subject to constraints: the customers belong to a social network. It also shows that social networks matter because equilibrium prices...

We consider the discrete time threshold-θ contact process on a random r-regular graph. We show that if θ≥2, r≥θ+2, ϵ1 is small and p≥p1(ϵ1), then starting from all vertices occupied the fraction of occupied vertices is ≥1−2ϵ1 up to time exp(γ1(r)n) with high probability. We also...