We model the competitive striving for high-level positions in firms by letting experimental participants compete in bidding for prizes of different sizes in a hierarchy. Our set-up includes both a flat hierarchy and a steep hierarchy. We mainly focus on whether men and women behave differently with respect to bidding for higher and lower positions, but also consider other possible sources of heterogeneity in behavior. On average, we find no statistically significant differences between women and men, except for the top position of the flat hierarchy, where women bid significantly higher. For lower positions, bids are generally close to optimal bidding whereas they are relatively lower for higher positions. Women do win the top positions significantly more often, but there are no significant gender differences in earnings, the difference between prizes and bids. Overall, we only find minor differences between women’s and men’s behavior. Our results suggest that the strong gender differences in attitudes towards competition that were found in numerous previous studies based on competition in tournaments with real-effort tasks may not carry over to other environments. A broader implication of our results thus is that a particular phenomenon should be studied using various experimental designs.