Gender-specific patterns of self-selection into competitive and cooperative environments may have multiple reasons. One of the most prominent explanations to this point is, that there are inherent differences between men and women when it comes to preferences regarding competition. We take a different point of view and claim that gender-task stereotypes are able to explain a large part of the under-representation of women in tournament like environments. We conduct an experiment with a quantitative task which has been shown to have a strong male connotation and a verbal task which we hypothesize to be gender neutral. After controlling for differences in performance, risk attitudes, and overconfidence, we find that women self-select significantly less into competition against men only in the quantitative task. This finding suggests that remaining gender differences for entry into competition are driven by gender-task stereotypes. As a robustness check, we explore the self-selection into incentive schemes given different gender compositions of groups and self-selection into single-sex groups given different incentive schemes. Furthermore, we report the results of a framed field experiment, where we explore a further task - throwing balls into a bucket - that has as well a male connotation. These additional results further strengthen our interpretation.