Social hierarchies are often found in group-living animals. The hierarchy position can influence reproductive success (RS), with a skew towards high-ranking individuals. The amount of aggression in social dominance varies greatly, both between species and between males and females within species. Using game theory we study this variation by taking into account the degree to which reproductive competition in a social group is mainly local to the group, emphasizing within-group relative RS, or global to a larger population, emphasizing an individual's absolute RS. Our model is similar to recent approaches in that reinforcement learning is used as a behavioural mechanism allowing social-hierarchy formation. We test two hypotheses. The first is that local competition should favour the evolution of mating or foraging interference, and thus of reproductive skew. Second, decreases in reproductive output caused by an individual's accumulated fighting damage, such as reduced parenting ability, will favour less intense aggression but should have little influence on reproductive skew. From individual-based simulations of the evolution of social dominance and interference, we find support for both hypotheses. We discuss to what extent our results can explain observed sex differences in reproductive skew and social dominance behaviour.