  This paper investigates the incentives of mobile network operators (MNOs) for
acquiring additional spectrum to offer mobile virtual network operators (MVNOs)
and thereby inviting competition for a common pool of end users (EUs). We
consider a base case and two generalizations: (i) one MNO and one MVNO, (ii)
one MNO, one MVNO and an outside option, and (iii) two MNOs and one MVNO. In
each of these cases, we model the interactions of the service providers (SPs)
using a sequential game, identify when the Subgame Perfect Nash Equilibrium
(SPNE) exists, when it is unique and characterize the SPNE when it exists. The
characterizations are easy to compute, and are in closed form or involve
optimizations in only one decision variable. We identify metrics to quantify
the interplay between cooperation and competition, and evaluate those as also
the SPNEs to show that cooperation between MNO and MVNO can enhance the payoffs
of both, while increased competition due to the presence of additional MNOs is
beneficial to EUs but reduces the payoffs of the SPs.
