In many social species, competition between groups is a major factor proximately affecting group-level movement patterns and space use and ultimately shaping the evolution of group living and complex sociality. Here we evaluated the factors influencing group-level dominance among 5 social groups of wild baboons (Papio cynocephalus), in particular focusing on the spatial determinants of dominance and the consequences of defeat. When direct conflict occurred between conspecific baboon groups, the winning group was predicted by differences in the number of adult males in each group and/or groups that had used the areas surrounding the encounter location more intensively than their opponent in the preceding 9 or 12 months. Relative intensity of space use over shorter timescales examined (3 and 6 months) was a poor predictor of the interaction's outcome. Losing groups but not winning groups experienced clear short-term costs. Losing groups used the area surrounding the interaction less following an agonistic encounter (relative to their intensity of use of the area prior to the interaction). These findings offer insight into the influences and consequences of intergroup competition on group-level patterns of space use.