This paper describes a game theoretical model of traffic where multiple drivers interact with each other. The model is developed using hierarchical reasoning, a game theoretical model of human behavior, and reinforcement learning. It is assumed that the drivers can observe only a partial state of the traffic they are in and therefore although the environment satisfies the Markov property, it appears as non-Markovian to the drivers. Hence, each driver implicitly has to find a policy, i.e. a mapping from observations to actions, for a Partially Observable Markov Decision Process. In this paper, a computationally tractable solution to this problem is provided by employing hierarchical reasoning together with a suitable reinforcement learning algorithm. Simulation results are reported, which demonstrate that the resulting driver models provide reasonable behavior for the given traffic scenarios.