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There is great interest in considering the energy efficiency aspect of wireless cellular networks. Coordinated multipoint (CoMP) communication is a new method that helps with the implementation of dynamic base station coordination for energy efficient communications. On the other hand, the power grid infrastructure is experiencing a significant shift from the traditional electricity grid to the smart grid. In this paper, we consider not only energy efficient communications but also the dynamics of the smart grid in designing green wireless cellular networks. We formulate the system as a Stackelberg game, which has two levels: a cellular network level and a smart grid level. Simulation results show that the smart grid has significant impacts on green wireless cellular networks, and our proposed scheme can significantly reduce operational expenditure and CO2 emissions in green wireless cellular networks.