There is great interest in considering the energy efficiency aspect of wireless cellular networks. When a wireless cellular network is powered by the smart grid, only considering energy efficiency in the cellular network is not enough. In this paper, the authors consider not only energy-efficient communications but also the dynamics of the smart grid in operating green wireless cellular networks. They formulate the system as a two-level Stackelberg game. A backward induction method is used to analyze the proposed scheme. They prove that the Stackelberg Equilibrium (SE) of the proposed game exists and is unique. An iteration algorithm is proposed to obtain the SE.