Human infants face the formidable challenge of learning the structure of their social environment. Previous research indicates that infants have early-developing representations of intentional agents, and of cooperative social interactions, that help meet that challenge. Here we report five studies with 144 infant participants showing that 10- to 13-month-old, but not 8-month-old, infants recognize when two novel agents have conflicting goals, and that they use the agents' relative size to predict the outcome of the very first dominance contests between them. These results suggest that preverbal infants mentally represent social dominance and use a cue that covaries with it phylogenetically, and marks it metaphorically across human cultures and languages, to predict which of two agents is likely to prevail in a conflict of goals.