We developed fast solver for constrained dynamic games and applied it to complex autonomous driving scenarios. The autonomous driving vehicle and the cars in its surroundings are agents participating in a game. Each vehicle has its own objective: reach a desired speed, drive on a certain lane etc. Additionally, the agents must respect constraints: avoiding collisions with other vehicles, respecting speed limits etc. The planner in the autonomous driving car solves this constrained game for a Nash equilibrium solution. This allows the autonomous driving vehicle to plan for itself and predict the trajectories of the cars in its surroundings jointly. We control the autonomous vehicle by executing this planner in a receding horizon loop at frequencies larger than 70 Hz. This model predictive control planner generates complex driving behaviors where vehicles negotiate and share the responsibility for avoiding collisions.