Equilibria in networks

We study a model in which two carriers choose networks to connect cities and compete for customers. We show that if carriers compete aggressively (e.g., Bertrand-like behavior), one carrier operating a single hub-spoke network is an equilibrium outcome. Competing hub-spoke networks are not an equilibrium outcome, although duopoly equilibria in nonhub networks can exist. If carriers do not compete aggressively, an equilibrium with competing hub-spoke networks exists as long as the number of cities is not too small. We provide conditions under which all equilibria consist of hub-spoke networks.