This paper proposes a model to ensure safe and realistic human-robot interaction for an autonomous vehicle interacting with a human-driven vehicle, by incorporating the driving style of the human driver. The interaction is modeled as a game, where both agents try to maximize future rewards. The driving style of the human is captured via the role of the human driver in the game, capturing the fact that humans with different driving styles reason differently. The solution of the game is obtained using an numerical approximation and used by the autonomous vehicle to plan optimally ahead. The model is validated via simulations on a safety-critical scenario, where realistic driving style-dependent behaviour emerges naturally.