Motivated by the growing popularity of both the services offered by the ride-hailing companies and the electric vehicles (EVs), we study a scenario in which a central body e.g., the government, wants to influence how the EVs of different ride-hailing companies spread among different charging stations by offering discounted prices of charging. Because the companies share the charging infrastructure, they inherently compete to minimize their expected total queuing times at the charging stations. From the perspective of Stackelberg and Inverse Stackelberg games we analyze two pricing mechanisms for the government that guarantee existence of a Nash equilibrium of the game played between the ride-hailing companies. We compare their performance in a case study based on taxi data from the city of Shenzhen and also show how the systems behave in terms of robustness.