The purpose of this paper is to show how key concepts from control theory, game theory, and mean field theory can be exploited to design joint control-allocation policies in cognitive wireless networks. One of the key features of the proposed approach is that transmitters (which are assumed to be cognitive and autonomous decisionnally speaking) have a certain knowledge of the channel evolution law and want to reach a certain transmission rate target while minimizing the energy consumed by the power supply and not the one corresponding to radio-frequency signals (which is known to be important to design green wireless networks). The optimal centralized policy is derived in order to have an upper bound on the performance of the decentralized system. Then, the Nash equilibrium of the cognitive network is determined by using recent results from mean field theory (MFT). In order to evaluate the performance gap between decentralized and centralized policies we introduce and evaluate the MFT-based asymptotic price of anarchy (APoA).