A hierarchical spatial game over licenced resources

We consider a scenario in which a regulator owns the spectrum in a region. Two service providers lease spectrum from the regulator and set up a base station each to serve mobile subscribers. This leads to a hierarchical game with players at two levels- the mobile subscribers at level 1 and the service providers at level 2. In the game at level 1, each mobile subscriber chooses a service provider to subscribe to and whether to be a primary subscriber of its service provider and receive high-priority service or to be a secondary subscriber and receive low-priority service. In the game at level 2, each service provider chooses the quantity of spectrum to lease from the regulator and the rates at which to charge its mobile subscribers for the throughput they receive. We first analyze the game at level 1 for different models and in each case show the existence of a threshold-type Wardrop equilibrium, in which there exist thresholds that divide the region into sets of mobile subscribers that make the same decision at equilibrium. Next, assuming that the mobile subscribers act so as to give rise to the equilibrium found above, we analyze the game at level 2 and show the existence of a Nash equilibrium.