When a two-choice "Simon task" is distributed between two people, performance in the shared go/no-go task resembles performance in the whole task alone. This finding has been described as the joint Simon effect (JSE). Unlike the individual go/no-go task, not only is the typical joint Simon task shared with another person, but also the imperative stimuli dictate whose turn it is to respond. Therefore, in the current study, we asked whether removing the agent discrimination component of the joint Simon task influences co-representation. Participants performed the typical joint Simon task, which was compared to two turn-taking versions of the task. For these turn-taking tasks, pairs predictably alternated turns on consecutive trials, with their respective imperative stimulus presented either on 100% of their turns (fully predictable group) or on 83% of their turns (response-uncertainty group, 17% no-go catch trials). The JSE was absent in the fully predictable, turn-taking task, but emerged similarly under the response-uncertainty condition and the typical joint Simon task condition where there is both turn and response-execution-related uncertainty. These results demonstrate that conflict related to agent discrimination is likely not a critical factor driving the JSE, whereas conflict surrounding the need to execute a response (and hence the degree of preparation) appears fundamental to co-representation.