Optimal Price Competition for Spectrum Sharing in Cognitive Radio: A Dynamic Game-Theoretic Approach

Optimal pricing for dynamic spectrum sharing in "cognitive radio" networks is an open research issue. In this paper, we address the problem of spectrum pricing in a cognitive radio environment in which multiple primary services with spectrum opportunity compete with each other to offer spectrum access to the secondary services. By using an optimal pricing scheme, each of the primary services aims to maximize its profit under quality of service (QoS) constraint. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. For a primary service/user, the QoS degradation is considered as the cost incurred for offering spectrum access to the secondary service/user. For the secondary service, we adopt a utility function to obtain the demand function. With a Bertrand game model, we are able to analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., optimal pricing adopted by the primary services). In addition, we present distributed iterative game algorithms to obtain the solution. The stability of the proposed iterative game algorithms in terms of convergence to the Nash equilibrium is studied.