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A parameter adaptively adjustable utility function based on the asymmetric sigmoid function is investigated for the non-cooperative power control game (NPCG) model in cognitive radio networks (CRN). Each secondary user (SU) can adaptively adjust the parameter to track along with the wireless interference environment for the optimal power strategy. From the fairness of view, a pricing function related to the channel gain of each SU is designed, which can improve the Pareto optimality of the Nash equilibrium solution (NES). A parallel utility function choosing approach for each SU is proposed according to channel state information (CSI) and the utility obtained at this time. The simulation results show that the proposed power control scheme achieves a better performance compared with the fixed utility function method, and the pricing function actually improves the optimality of the NES.