In this paper, we study the competitive interactions between electric vehicle charging stations (EVCSs) with renewable electricity generation facilities (REGFs). As electric vehicles (EVs) become more popular, there will be a competition between neighboring EVCSs to attract more EVs. Therefore, an EVCS is likely to set its electricity price by taking into account the competition with neighboring EVCSs, such that its revenue is maximized. We model the competitive interactions between EVCSs by using game theory. In this paper, we show that the game played by EVCSs is a supermodular game and there exists a unique pure Nash equilibrium for best response algorithms with arbitrary initial policy. Simulation results confirm the convergence of the game between EVCSs. The results also verify that it is beneficial for both EVs and EVCSs to have REGFs and all EVCSs will have REGFs in the long run.