Cournot and Bertrand Game Models for a Simple Spectrum Sharing Framework in Cognitive Radio Networks

Cognitive radio technology has been proposed to achieve a more efficient spectrum usage by using spectrum opportunities in time, frequency and space which is not fully used by a licensed system (primary system), but without disturbing the primary system. In this paper, we address the problem of spectrum sharing among one primary user and two secondary users. We model this problem as a game and use Cournot and Bertrand game models for spectrum allocation to secondary users. In each game model we first present the formulation of static cases when the secondary users can observe the adopted strategies and the payoff of each other. However, this assumption may not be realistic in some cognitive radio systems. Therefore, we formulate dynamic approaches in which the secondary users just communicate with the primary user. The stability conditions of the dynamic behavior for these spectrum sharing schemes is investigated