Pricing Game With Complete or Incomplete Information About Spectrum Inventories for Mobile Virtual Network Operators

In network virtualization, mobile virtual network operators (MVNOs) lease spectrum resources from mobile network operators (MNOs) and offer certain wireless services to end users. Each MVNO competes with others using optimal price and spectrum inventory so as to profit. However, the inventory of one MVNO is private information and maybe unknown to others, which makes pricing decisions difficult for MVNOs. In this work, we first study the pricing strategy given others' inventory information. We model the pricing decision problem using the non-cooperative game theory, and develop an optimal price setting algorithm based on an ordinal potential game. Then we put forward three cooperation strategies for MVNOs and analyze the impacts of the coalitions structure on pricing decision. For the situation where the inventory of one MVNO is unknown to others, we use the Bayesian coalition formation game to formulate the pricing decision problem and propose an optimal price setting algorithm based on the Minimum Mean-Square Error to resolve the conflicts resulting from the uncertainty. Next we define a Belief Pareto Order to characterize the preferences of MVNOs regarding the coalition structures. Then we devise a distributed coalition formation algorithm with the proposed belief Pareto order to achieve a Bayesian-Nash stable coalition structure that enables each MVNO to maximize its own revenue. Finally, simulation results demonstrate comprehensive performance evaluation of the proposed game model and provide a guidance on pricing strategies for MVNOs.