A game-theoretic approach for energy-efficient power control in spectrum sharing networks

In this paper, we study energy-efficient power control for spectrum-sharing networks, where multiple systems of transmitting nodes share the same spectrum. In the spectrum sharing networks, reducing the transmit power of one system is always beneficial to the energy efficiencies (EEs) of the other systems. However, reducing the transmit power may not be always optimal in maximizing the EE of a system. These conflicting interests among the systems are molded by a non-cooperative energy-efficient power control game, where each system chooses its transmit power to maximize its own EE. We prove the existence and uniqueness of the Nash equilibrium of this game. However, due to the selfish behaviors of the systems in the network, the Nash equilibrium is in general inefficient. To improve the EE of the Nash equilibrium, we incorporate pricing to the non-cooperative energy-efficient power control game. For the spectrum sharing network consisting of two systems, we find a sufficient condition on the transmit powers of the systems assuring the pricing-based game to be a supermodular game, which always admits at least one Nash equilibrium.