Wireless operators in a shared spectrum

So far, cellular networks have been operated in "private" frequency bands. But recently, several researchers and legislators have argued in favor of a more flexible and more efficient management of the spectrum, leading to the possible coexistence of several network operators in a shared frequency band. In this paper, we study this situation in detail, assuming that mobile devices can freely roam among the various operators. Free roaming means that the mobile devices measure the signal strength of the pilot signals (i.e., beacon signals) of the base stations and attach to the base station with the strongest pilot signal. We model the behavior of the network operators in a game theoretic setting in which each operator decides about the power of the pilot signal of its base stations. We first identify possible Nash equilibria in the theoretical setting in which all base stations are located on the vertices of a two-dimensional lattice. We then relax this topological assumption and show that, in the more general case, finding the Nash equilibria is an NP-complete problem. Finally, we prove that a socially optimal Nash equilibrium exists and that it can be enforced by using punishments.