A Stackelberg approach for energy efficient multi-carrier systems

We address a hierarchical game-theoretic model for studying power control in multi-carrier systems. The power control problem is modeled as a Stackelberg game where transmitters choose their control policy selfishly in order to maximize their individual energy efficiency. We establish the existence of the Stackelberg equilibrium and give its formal expression. Interestingly, we show that, under some assumptions, introducing a certain degree of hierarchy in a multi-carrier system results in a kind of coordination game where the primary and the secondary users have incentive to choose their transmitting carriers in such a way that they always transmit on orthogonal channels. Such an important result offers insights into how to design hierarchy in multi-carrier environments. Numerical results validate our theoretical claims.