Behavioral coordination is involved in many forms of primate interactions. Co-representation is the simultaneous mental representation of one’s own and the partner’s task and actions. It often underlies behavioral coordination and cooperation success. In humans, the dyadic social context can modulate co-representation. Here, we first investigated whether individual differences in co-representation in the joint Simon task in capuchin monkeys and Tonkean macaques can be explained by social factors, namely dyadic grooming and sociality index, rank difference and eigenvector centrality. These factors did not predict variation in co-representation. However, in this specific task, co-representation reduces rather than facilitates joint performance. Automatic co-representation therefore needs to be inhibited or suppressed to maximize cooperation success. We therefore also investigated whether general inhibitory control (detour-reaching) would predict co-representation in the joint Simon task in Tonkean macaques, brown capuchin and marmoset monkeys. Inhibitory control did neither explain individual differences nor species differences, since marmosets were most successful in their joint performance despite scoring lowest on inhibitory control. These results suggest that the animals’ ability to resolve conflicts between self and other representation to increase cooperation success in this task is gradually learned due to frequent exposure during shared infant care, rather than determined by strong general inhibitory control. Further, we conclude that the joint Simon task, while useful to detect co-representation non-invasively, is less suitable for identifying the factors explaining individual differences and thus a more fruitful approach to identify these factors is to design tasks in which co-representation favors, rather than hinders cooperation success.