In this paper, we have introduced two models for spectrum management (spectrum trading and spectrum competition) in cognitive radio network. The first model is without game theory and the second one is with game theory. The first model for spectrum management without game theory, called SMWG, which has been designed to provide an efficient and dynamic equations to enhance the network performance. SMWG provides a novel function, called QoS function, to support three levels of QoS. In addition, it provides a novel factor, called Competition Factor, to control the behaviors among spectrum owners (primary users). In the second model, we have applied the game theory concept into spectrum management (SMG) to compare the network performance in both cases (SMWG and SMG). SMG provides two games, the first one is to model the dynamic behavior of spectrum competition among primary users, a Bertrand game is formulated where the Nash equilibrium is considered as the solution. The second game is to model the spectrum trading between the primary user and the secondary user, a Stackelberg game is formulated where the Nash equilibrium is again considered as the solution. Basically, the solution is found in terms of the size of the offered spectrum to the secondary users with regards to the offered spectrum price. We compare SMWG with conventional scheme, also compare SMG with conventional scheme, and finally compare SMWG with SMG in terms of network performance.