Competition over scarce resources is common across the animal kingdom. Here we investigate the strategies of chimpanzees and children in a limited resource problem. Both species were presented with a tug-of-war apparatus in which each individual in a dyad received a tool to access a reward, but tools could not be used simultaneously. We assessed the equality of tool use as well as the frequency of turn taking. Both species managed to overcome this conflict of interest but used different strategies to do so. While there was substantial variation in chimpanzee behaviour, monopolization was the common course of action: tool use was asymmetric with individual chimpanzees monopolizing the resource. In children, turn-taking emerged as the dominant strategy: tool use was symmetric and children alternated access to the tool at a high rate. These results suggest that while both species possess strategies for solving limited resource problems, humans might have evolved species unique motivations and socio-cognitive skills for dealing with such conflicts of interest.