This paper uses a game of strategic interaction to simulate entry and location of fast charging stations for electric vehicles. It evaluates the equilibria obtained in terms of social welfare and firm spatial differentiation. Using Barcelona mobility survey, demographic data and the street graph we find that only at an electric vehicle penetration rate above 3% does a dense network of stations appear as the equilibrium outcome of a market with no fiscal transfers. We also find that price competition drives location differentiation measured not only in Euclidean distances but also in consumer travel distances.