According to sexual selection theory, the sexes are faced with opposing evolutionary goals. Male fitness benefits from access to females, whereas female fitness is constrained by food resources and safety for themselves and their offspring. Particularly in large solitary carnivores, such as polar bears (Ursus maritimus), these divergent goals can potentially lead to conflict between the sexes. Outside the mating season, when polar bears are on the move across vast distances, the consequences of such conflict can become apparent when individuals arrive at the same food source. To investigate interrelationships between the sexes, we observed successive polar bears visiting a bird breeding colony to feed on clutches of eggs. We found that males succeeded females more frequently and more closely than expected by chance. Moreover, when males were closer to conspecifics, they walked faster, spent less time in the colony and ingested less food. In contrast, female foraging performance was not associated with proximity to other bears. Irrespective of proximity, females generally spent short periods in the colony and ingested fewer clutches than males. Our results suggest that in polar bears, there is a trade-off between the benefits of food intake and the opportunities (in males) and risks (in females) posed by encountering conspecifics.