Price and Spectrum Inventory Game for MVNOs in Wireless Virtualization Communication Markets

In wireless virtualization communication markets, mobile virtual network operators (MVNOs) lease spectrum resources from mobile network operators (MNOs) and offer certain wireless services to end users. In order to attract more users, one MVNO may provide better service (i.e., more spectrum inventory thus higher QoS) and/or set lower retail price through taking its competitors' decisions into account. In this paper, we study the price strategy and spectrum inventory decision for MVNOs to optimize profits. First, we integrate these price and inventory factors into the utility function of end users and the revenue function of MVNOs, respectively, and analyze the impacts of the price factor on profits given each MVNO's inventory. With non-cooperative game theory, we derive the Cournot Nash equilibrium (C-NE) and further reveal several effective conclusions with guidance on price decision. Significantly, we discover that the increase of one MVNO's inventory would reduce others' revenues even though they adjust their prices to the C-NEs. Based on this observation, we propose to consider the price strategy and inventory decision together. Specifically, for a duopoly MVNOs market, we develop an ordinary differential equation (ODE) based evolutionary model that only contains its own price and inventory, which is very helpful for further analysis. However, since there is no explicit expression for the ODE, we figure out the boundary condition and initial value to facilitate a numerical solution. Overall, the conclusions in this study provide insights into price and inventory decision, and simulation results also validate our analysis.