In this paper, we propose an algorithmic perspective of the Stackelberg game model introduced in [1] applied to cognitive radio networks (CRN). Typically, we assume that individual users attempt to access to the wireless spectrum while maximizing their individual energy efficiency. Having looked at the main properties of the proposed energy efficient and in particular the one related to spectrum coordination, we address the problem of sensing. Then, we provide a deep algorithmic analysis on how primary and secondary users can reach such a spectrum coordination using an appropriate learning process. We validate our results through extensive simulations and compare the proposed algorithm to some typical scenarios including the non-cooperative case in [2] and the throughput-based-utility systems. Specifically it is shown that the proposed Stackelberg decision approach maximizes the energy efficiency while still optimizing the throughput at the equilibrium.