This paper examines the interconnections between the power and transportation networks from a game theoretic perspective. Electric vehicle travelers choose the lowest-cost routes in response to the price of electricity and traffic conditions, which in turn affects the operation of the power and transportation networks. In particular, discrete choice models are utilized to describe the behavioral process of electric vehicle drivers. A game theoretic approach is employed to describe the competing behavior between the drivers and power generation units. The power-traffic network equilibrium is proved to possess a potential type structure, which establishes the properties of the network equilibrium. Moreover, the network equilibrium state is shown to be a welfare-maximizing operating point of the electric distribution network considering the spatial demand response of electric vehicle loads. A decentralized algorithm based on the optimality condition decomposition technique is developed to attain the equilibrium flow solutions. Numerical experiments demonstrate how the proposed framework can be used to alleviate both power and traffic congestion.