When sharing a task with another person that requires turn taking, as in doubles games of table tennis, performance on the shared task is similar to performing the whole task alone. This has been taken to indicate that humans co-represent their partner's task share, as if it were their own. Task co-representation allows prediction of the other's responses when it is the other's turn, and leads to response conflict in joint interference tasks. However, data from our lab cast doubt on the view that task co-representation and resulting response conflict are the only or even primary source of effects observed in task sharing. Recent findings furthermore suggest another potential source of interference in joint task performance that has been neglected so far: Self-other discrimination and conflict related to agent identification (i. e., determining whether it is "my" or the other's turn). Based on these findings we propose that participants might not always co-represent what their partner is supposed to do, but instead co-represent that another agent is responsible for part of the task, and when it is his turn. We call this account the actor co-representation account.