Mobile Virtual Network Operators (MVNOs) are an increasingly growing segment of the market for wireless services. MVNOs do not own their own network infrastructure and so must cooperate with existing Mobile Network Operators (MNOs) to gain access to the network infrastructure needed to enter this market. Cooperating with an MVNO is a non-trivial decision for an MNO in part because the MVNO may then become a potential competitor for customers. One motive for entering into such an arrangement is that the MVNO receives an added value from serving customers beyond what it earns from charging them for wireless service. We study a game theoretic model for the cooperation and competition between an MNO and such an added value MVNO based on models for price competition with congestible resources. Our model captures two different dimensions of how an MNO may cooperate. The first dimension is the payment scheme between the MNO and the MVNO. The second dimension is the access priority that the MNO chooses to offer to the MVNO's customers. We characterize the pros and cons of different cooperation modes and analyze the optimal cooperation mode under different conditions.