Across taxa, males employ a variety of mating strategies, including sexual coercion and the provision, or trading, of resources. Biological market theory (BMT) predicts that trading of commodities for mating opportunities should exist only when males cannot monopolize access to females and/or obtain mating by force, in situations where power differentials between males are low; both coercion and trading have been reported for chimpanzees (Pan troglodytes). Here, we investigate whether the choice of strategy depends on the variation in male power differentials, using data from two wild communities of East African chimpanzees (Pan troglodytes schweinfurthii): the structurally despotic Sonso community (Budongo, Uganda) and the structurally egalitarian M-group (Mahale, Tanzania). We found evidence of sexual coercion by male Sonso chimpanzees, and of trading—of grooming for mating—by M-group males; females traded sex for neither meat nor protection from male aggression. Our results suggest that the despotism–egalitarian axis influences strategy choice: male chimpanzees appear to pursue sexual coercion when power differentials are large and trading when power differentials are small and coercion consequently ineffective. Our findings demonstrate that trading and coercive strategies are not restricted to particular chimpanzee subspecies; instead, their occurrence is consistent with BMT predictions. Our study raises interesting, and as yet unanswered, questions regarding female chimpanzees’ willingness to trade sex for grooming, if doing so represents a compromise to their fundamentally promiscuous mating strategy. It highlights the importance of within-species cross-group comparisons and the need for further study of the relationship between mating strategy and dominance steepness.