Competitive spectrum sharing in cognitive radio networks: a dynamic game approach

"Cognitive radio" is an emerging technique to improve the utilization of radio frequency spectrum in wireless networks. In this paper, we consider the problem of spectrum sharing among a primary user and multiple secondary users. We formulate this problem as an oligopoly market competition and use a noncooperative game to obtain the spectrum allocation for secondary users. Nash equilibrium is considered as the solution of this game. We first present the formulation of a static game for the case where all secondary users have the current information of the adopted strategies and the payoff of each other. However, this assumption may not be realistic in some cognitive radio systems. Therefore, we consider the case of bounded rationality in which the secondary users gradually and iteratively adjust their strategies based on the observations on their previous strategies. The speed of adjustment of the strategies is controlled by the learning rate. The stability condition of the dynamic behavior for this spectrum sharing scheme is investigated. The numerical results reveal the dynamics of distributed dynamic adaptation of spectrum sharing strategies.