Humans are highly co‐operative and thus cognitively, affectively, and motivationally tuned to pursue shared goals. Yet, cooperative tasks typically require people to constantly take and switch individual roles. Task relevance is dictated by these roles and thereby dynamically changing. Here, we designed a dyadic game to test whether the family of P3 components can trace this dynamic allocation of task relevance. We demonstrate that late positive event‐related potential (ERP) modulations not only reflect predictable asymmetries between receiving and sending information but also differentiate whether the receiver's role is related to correct decision making or action monitoring. Furthermore, similar results were observed when playing the game with a computer, suggesting that experimental games may motivate humans to similarly cooperate with an artificial agent. Overall, late positive ERP waves provide a real‐time measure of how role taking dynamically shapes the meaning and relevance of stimuli within collaborative contexts. Our results, therefore, shed light on how the processes of mutual coordination unfold during dyadic cooperation.