For numerical simulations of crowd dynamics in an evacuation we need a computationally light environment, such as the cellular automaton model (CA). By choosing the right model parameters, different types of crowd behavior and collective effects can be produced. But the CA does not answer why, when, and how these different behaviors and collective effects occur. In this article, we present a model, where we couple a spatial evacuation game to the CA. In the game, an agent chooses its strategy by observing its neighbors' strategies. The game matrix changes with the distance to the exit as the evacuation conditions develop. In the resulting model, an agent's strategy choice alters the parameters that govern its behavior in the CA. Thus, with our model, we are able to simulate how evacuation conditions affect the behavior of the crowd. Also, we show that some of the collective effects observed in evacuations are a result of the simple game the agents play.