A decentralized network of cognitive and non-cognitive transmitters where each transmitter aims at maximizing his energy-efficiency is considered. The cognitive transmitters are assumed to be able to sense the transmit power of their non-cognitive counterparts and the former have a cost for sensing. The Stackelberg equilibrium analysis of this $2-$level hierarchical game is conducted, which allows us to better understand the effects of cognition on energy-efficiency. In particular, it is proven that the network energy-efficiency is maximized when only a given fraction of terminals are cognitive. Then, we study a sensing game where all the transmitters are assumed to take the decision whether to sense (namely to be cognitive) or not. This game is shown to be a weighted potential game and its set of equilibria is studied. Playing the sensing game in a first phase (e.g., of a time-slot) and then playing the power control game is shown to be more efficient individually for all transmitters than playing a game where a transmitter would jointly optimize whether to sense and his power level, showing the existence of a kind of Braess paradox. The derived results are illustrated by numerical results and provide some insights on how to deploy cognitive radios in heterogeneous networks in terms of sensing capabilities.