  In this paper, we propose a hierarchical game approach to model the energy
efficiency maximization problem where transmitters individually choose their
channel assignment and power control. We conduct a thorough analysis of the
existence, uniqueness and characterization of the Stackelberg equilibrium.
Interestingly, we formally show that a spectrum orthogonalization naturally
occurs when users decide sequentially about their transmitting carriers and
powers, delivering a binary channel assignment. Both analytical and simulation
results are provided for assessing and improving the performances in terms of
energy efficiency and spectrum utilization between the simultaneous-move game
(with synchronous decision makers), the social welfare (in a centralized
manner) and the proposed Stackelberg (hierarchical) game. For the first time,
we provide tight closed-form bounds on the spectral efficiency of such a model,
including correlation across carriers and users. We show that the spectrum
orthogonalization capability induced by the proposed hierarchical game model
enables the wireless network to achieve the spectral efficiency improvement
while still enjoying a high energy efficiency.
