Familiarity influences individual decision-making in many vertebrate species. Here, we propose that familiarity modulates behaviour to different extents depending on the social context of the interaction. Specifically, the more that one player stands to gain relative to the other, the less important familiarity will be in influencing their responses to one another. We test this prediction using pairs of male guppies (Poecilia reticulata) in three competitive scenarios of increasing asymmetry in outcome to the two players: schooling under potential threat (similar outcomes), competing for a defensible food source (some asymmetry) and competing for a receptive female (strongly asymmetrical outcomes). Males show a graded response as asymmetry increases, with familiarity producing marked behavioural differences under potential threat, minor changes when competing for food, but none at all in competition for mating opportunities. This suggests that mutualistic benefits can arise as a by-product of selfish behaviour, supporting the role of pseudo-reciprocity in the evolution of cooperation.