One of the truisms of the neo-paleo-conventional wisdom on gender is that women are less competitive than men. They choose non-competitive activities when given a choice, and don't enjoy competition the way men do when they have to compete. They particularly don't like to compete against men.
So, is it true?
A couple of interesting studies casting doubt on this proposition:
Gender differences in preferences for competition may have a large cultural component. Among the Khasi, a matrileneal and quasi-matriarchal culture in India, women are more likely than men to select competitive tasks and environments.
Women's competition aversion may also be peculiar to activities in which men are commonly perceived to excel more than women. In other words, it may be related to "stereotype threat."
Is this the final word? Does this prove that there are no inherent differences between men and women in level of (and enjoyment of) competitiveness? No, of course not. It's just an interesting challenge to conventional wisdom.