Experiments indicate that one of the main forces in pedestrian dynamics is collision avoidance. In other words individuals actively anticipate the future to predict a possible collision time and adjust their velocity accordingly. At the same time they show no intention to change their direction when walking close to each other in the same direction. This collision avoidance behavior plays a major role in pedestrian dynamics, which w as already illustrated in numerical ​​simulations. The simulations show that already a simple dynamical systems model, with forces​​depending on the estimated hitting time reproduce complex dynamics such as velocity alignment. In this talk we propose a different model, motivated from optimal control theory, which is based on a simple two-player pursuer evader game. We shall use Bellman’s approach to study the embedded multi-player game for collision avoidance and discuss related theoretical as well as numerical aspects. Joint work with Marie-Therese Wolfram.