Stochastic Game for Wireless Network Virtualization

We propose a new framework for wireless network virtualization. In this framework, service providers (SPs) and the network operator (NO) are decoupled from each other: The NO is solely responsible for spectrum management, and SPs are responsible for quality-of-service (QoS) management for their own users. SPs compete for the shared wireless resources to satisfy their distinct service objectives and constraints. We model the dynamic interactions among SPs and the NO as a stochastic game. SPs bid for the resources via dynamically announcing their value functions. The game is regulated by the NO through: 1) sum-utility optimization under rate region constraints; 2) enforcement of Vickrey-Clarke-Groves (VCG) mechanism for pricing the instantaneous rate consumption; and 3) declaration of conjectured prices for future resource consumption. We prove that there exists one Nash equilibrium in the conjectural prices that is efficient, i.e., the sum-utility is maximized. Thus, the NO has the incentive to compute the equilibrium point and feedback to SPs. Given the conjectural prices and the VCG mechanism, we also show that SPs must reveal their truthful value functions at each step to maximize their long-term utilities. As another major contribution, we develop an online learning algorithm that allows the SPs to update the value functions and the NO to update the conjectural prices iteratively. Thus, the proposed framework can deal with unknown dynamics in traffic characteristics and channel conditions. We present simulation results to show the convergence to the Nash equilibrium prices under various dynamic traffic and channel conditions.