This paper experimentally investigates if and how people's competitiveness depends on their own gender and on the gender of people with whom they interact. Participants are given information about the gender of the co-participant they are matched with, they then choose between a tournament or a piece rate payment scheme, and finally perform a real task. As already observed in the literature, we find that significantly more men than women choose the tournament. The gender of the co-participant directly influences men's choices (men compete less against other men than against women), but only when the gender information is made sufficiently salient. A higher predicted competitiveness of women induces more competition. Giving stronger tournament incentives, or allowing the participants to choose the gender of their co-participant, increases women's willingness to compete, but does not close the gender gap in competitiveness.