Competition between primary and secondary operators with spectrum leasing and optimal spectrum subscription by Users

In this paper, a scenario is proposed where a mobile operator owning a spectrum license leases part of the spectrum to a secondary operator and also competes against it for users. Users can choose to subscribe to either operator and they subscribe the optimal amount of spectrum. This scenario is modeled using Game Theory as a two-stage game. In the first stage both operators play a one-shot simultaneous game and the Nash equilibrium is used. In the second stage, the Wardrop equilibrium is used assuming optimal choice in spectrum subscription by users. The model is solved using background induction. Results show the conditions under which perfect equilibrium exists, and two scenarios are identified, depending on the amount of spectrum that is available. The results are assessed from the point of view of the operator´s profits, from the user welfare and from the total welfare. Based on this assessment, arguments are presented justifying the intervention of a Regulatory Authority to enforce the entry of an operator.