Despite empirical evidence that women’s presence in management positions is a source of value co-creation for firms, these positions are still male-dominated. Some evidence from experimental economics suggests that one reason for this imbalance is that women shy away from competition. However, most of these studies have focused on competition systems that pit individuals against each other. We present an economic laboratory experiment that compares competition against others with competition against a set target. The crucial difference is that whereas the former involves competing against opponents, the latter does not. Our results show that significantly more women are willing to compete against a set target than against others. Furthermore, there is no reduction in men’s participation and no general efficiency reduction. Our findings suggest that firms that aim at value co-creation and sustainability through a gender-neutral promotion mechanism should introduce competition against a set target and reduce competition against others. This paper contributes to dispelling stereotypes about women’s reluctance to compete.