  A network of cognitive transmitters is considered. Each transmitter has to
decide his power control policy in order to maximize energy-efficiency of his
transmission. For this, a transmitter has two actions to take. He has to decide
whether to sense the power levels of the others or not (which corresponds to a
finite sensing game), and to choose his transmit power level for each block
(which corresponds to a compact power control game). The sensing game is shown
to be a weighted potential game and its set of correlated equilibria is
studied. Interestingly, it is shown that the general hybrid game where each
transmitter can jointly choose the hybrid pair of actions (to sense or not to
sense, transmit power level) leads to an outcome which is worse than the one
obtained by playing the sensing game first, and then playing the power control
game. This is an interesting Braess-type paradox to be aware of for
energy-efficient power control in cognitive networks.
