Oligopoly Bertrand model for price competition in cognitive radio networks

This paper presents a bandwidth allocation and pricing framework for the spectrum underlay in cognitive radio networks. We assume that a cognitive radio network containing a set of primary users coexists with secondary users in an underlay spectrum sharing paradigm. Primary users use licensed bands of the spectrum while secondary users choose among the bands available on sale based on their prices. By using a oligopoly, primary users in Bertrand´s theoretic model participate in a non-cooperative game with secondary users in spectrum buying. As a result, the Bertrand model´s oligopoly provides the equilibrium that is the best response correspondence between the primary users. In this type of game, primary users can maximise their own utility function, while secondary users can select resources that hold their minimum payment for buying bandwidth. The simulation results show that the proposed model can be used to solve the spectrum-buying problem for secondary users in cognitive radio networks.