Joint Operator Pricing and Network Selection Game in Cognitive Radio Networks: Equilibrium, System Dynamics and Price of Anarchy

This paper addresses the joint pricing and network selection problem in cognitive radio networks (CRNs). The problem is formulated as a Stackelberg game, where the primary and secondary operators (POs and SOs) first set the network subscription price to maximize their revenue. Then, users perform the network selection process, deciding whether to pay more for a guaranteed service or to use a cheaper best-effort secondary network, where congestion and low throughput may be experienced. We derive optimal stable price and network selection settings. More specifically, we use the Nash equilibrium concept to characterize the equilibria for the price setting game. On the other hand, a Wardrop equilibrium is reached by users in the network selection game since, in our model, a large number of users must individually determine the network to which they should connect. Furthermore, we study network users' dynamics using a population game model, and we determine its convergence properties under replicator dynamics, which is a simple yet effective selection strategy. Numerical results demonstrate that our game model captures the main factors behind cognitive network pricing and network selection, thus representing a promising framework for the design and understanding of CR systems.