Social primates constantly face situations in which their preferences collide and they need to engineer strategies to overcome conflicts of interest. Studies with chimpanzees, Pan troglodytes, have found that they use competitive strategies to overcome social dilemmas, maximizing their own benefits while minimizing the loss of rewards. However, little is known about how other primates that rely more on cooperation would overcome similar dilemmas. We therefore presented male–female pairs of common marmosets, Callithrix jacchus (cooperative breeders) with two experiments of an action-based paradigm that creates a conflict of interest over access to an unequal reward distribution. Rather than engaging in mutual defection, marmosets were able to overcome this social dilemma over time, by developing a mix of strategic behaviours (predominantly by females) and tolerance to disadvantageous reward distributions (predominantly by males). This mix of behavioural strategies yielded more and better rewards for the females. Importantly, such a net outcome is consistent with the natural history of this species where females, who carry a high energetic burden of reproduction, tend to be less prosocial and are receivers, rather than donors, in food-sharing events among adults.