An optimal pricing scheme to improve transmission opportunities for a mobile virtual network operator

Selling spectrum resources to mobile virtual network operators (MVNOs) is popular among primary network operators (POs) for increasing licensed spectrum utilization. An MVNO seeks transmission opportunities (TXOPs) on the PO’s licensed spectrum channel(s) by spectrum sensing. Since licensed primary users (PUs) often have higher transmission priority, TXOPs available to the MVNO are directly determined by PUs’ transmission behaviors. In this paper, we present the first study that uses a pricing scheme to regulate PUs’ transmission behaviors so that TXOPs for an MVNO are improved, meanwhile quality-of-service (QoS) of PUs can be guaranteed as well. Our idea is to design a non-uniform pricing scheme that regulates PUs to transmit based on a time-varying non-uniform transmission cost. We model the optimal pricing problem as a hierarchical game where the interaction between the PO and PUs is modeled as a Stackelberg game and the spectrum random access among PUs is modeled as a non-cooperative game. We first solve the non-cooperative game among PUs, as a building block, then we embed its outcome to a Markov Chain Monte Carlo (MCMC) framework to solve the whole optimal pricing problem. We strictly shows that there could be multiple optimal pricing schemes for a PO. Comprehensive simulations confirm the theoretical analysis, and valid the effectiveness of our proposed scheme.