Electric vehicles have been promoted by worldwide policy makers as a solution to combat environmental problems and stimulate economy, whereas the lack of extreme fast charging infrastructure has become one main obstacle to broad adoption of electric vehicles. The widespread of electric vehicles and extreme fast charging infrastructure would impact transportation systems, such as mobility, congestion, equity, toll revenue, and infrastructure maintenance needs. Effective planning must be able to predict the impact of projects and policies decades into the future. This study develops mathematical models to quantitatively analyze this complicated and important problem. In particular, we utilize game theory to understand the dependency between the choices made by travelers, and the congestion and delay in the system with respect to traffic assignment.