Bandwidth optimization in hetnets with competing service providers

We consider a wireless network in which multiple Service Providers (SPs) compete to provide both macrocell and femtocell services in different bands. There are two types of users: mobile users that can only connect to macrocells, and fixed users that can be served by both macrocells and femtocells. For a given allocation of bandwidths across SPs, we characterize for each SP the optimal bandwidth split across the macro- and femtocells along with the equilibrium prices. We show that there exists a unique Nash equilibrium wherein for each SP, macrocells only serve mobile users while femtocells only serve fixed users. All possible Nash equilibria for different system parameters are sorted into four categories corresponding to whether or not different SPs assign bandwidth to the macro- and/or femtocells. In addition, we characterize properties of each category. The equilibrium prices and macro/femto bandwidths can be computed via a series of best response updates, which is proven to converge. Conditions are also given that guarantee optimal social welfare as the number of SPs tends to infinity. Numerical results are presented to illustrate how the Nash equilibrium can change as a function of SP bandwidths.