We studied collaborative skill acquisition in a dynamic setting with the game Co-op Space Fortress. While gaining expertise, the majority of subjects became increasingly consistent in the role they adopted without being able to communicate. Moreover, they acted in anticipation of the future task state. We constructed a collaborative skill acquisition model in the cognitive architecture ACT-R that reproduced subject skill acquisition trajectory. It modeled role adoption through reinforcement learning and predictive processes through motion extrapolation and learned relevant control parameters using both a reinforcement learning procedure and a new to ACT-R supervised learning procedure. This is the first integrated cognitive model of collaborative skill acquisition and, as such, gives us valuable insights into the multiple cognitive processes that are involved in learning to collaborate.