  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. Keywords: Power Control, Stackelberg
Equilibrium, Energy-Efficiency.
