The case for a competitive market operated by a Mobile Network Operator (MNO) and a Mobile Virtual Network Operator (MVNO) is analysed in the paper. The resource that is leased by the MNO to the MVNO is spectrum. The MNO and the MVNO compete a la Bertrand ' posting subscription prices and the mobile users may choose to subscribe to one operator. The scenario is modeled by a three-level game comprising a bargaining game, which models the spectrum leasing by the MNO; a competition game, which models the price competition between the MNO and the MVNO; and a subscription game, which models the subscription choice by the mobile users, and the outcome of which may be either not to subscribe, to subscribe to the MNO or to subscribe to the MVNO. The game is solved through backward induction, and each level has a specific solution concept: Shapley value, for the bargain; Nash equilibrium, for the competition; and Wardrop equilibrium, for the subscription. The paper assesses which conditions lead to an equilibrium where the competition does take place, which are expressed as restrictions for the spectrum leasing price agreed at the bargaining, and the spectrum efficiency improvement achieved by the MVNO. Furthermore, it argues that the amount of the leased spectrum should be fixed exogenously in order to achieve optimal user and social welfares.