Group-living animals often do not maintain territories, but instead have highly overlapping ranges, even though in principle these are economically defendable. We investigate whether this absence of range defence reflects a collective action problem, since a territory can be considered a public good. In a comparative analysis comprising 135 primate species, we find a positive association between range overlap and group size, controlling for economic defendability and phylogenetic non-independence. We subsequently demonstrate that groups with multiple adults of both sexes suffer levels of range overlap twice as high as groups with only a single adult representative of either sex, consistent with the presence of a collective action problem. Finally, we reveal that this collective action problem can be overcome through philopatry of the larger sex. These results suggest that a social complication of group living is a stronger determinant of between-group relations among social animals than ecological factors, but also that collective defence is still achieved where the dominant sex is philopatric and effective defence is critical to reproductive success and survival. In addition, our findings support the idea that human-like warfare, defined as escalated collective territorial conflict, has an evolutionary basis reflected by cases of convergent evolution among non-human primates.