Recent studies have been conducted to indicate the ineffective usage of licensed bands due to the static spectrum allocation. In order to improve the spectrum utilization, the cognitive radio is therefore suggested to dynamically exploit the opportunistic primary frequency spectrums. The interference from the secondary users to the primary user consequently draws the attention to the spectrum and power management for the cognitive radio networks. In this paper, the constrained stochastic games are utilized to exploit the optimal policies for power management by considering the variations from both the channel gain and the primary traffic. Both the underlay and overlay waveforms are considered within the network scenarios for the proposed power management scheme. Constraints for allowable interferences will be applied in order to preserve the communication quality among the primary and the secondary users. According to the formulation of the constrained stochastic games, the existence of the constrained Nash equilibrium will be validated with rigorous proofs, which will be acquired as the optimal policies for the power management problem. Simulation results further validate the correctness of the theoreticallyderived policies for dynamic power management.