In 2003
Gneezy, Niederle, and Rustichini (pdf) examined a possible explanation for the gender gap in high-ranking positions. They compared the performance of men and women in non-competitive environments, in same-sex competitive environments, and in mixed-sex competitive environments. Performance in both the same-sex competitive and non-competitive environments was not significantly different for men and women, but in the mixed-sex competitive environment, the gender gap appeared. However, it is notable that the women's performance did not significantly decrease. The men's performance increased when they were pitted against women.
Shakib and Dunbar (2003) performed a series of interviews with high-school athletes that may explain some of this. The boys mentioned repeatedly how traumatizing it could be to lose to a girl. One boy described how a friend who was beaten by a girl gave up playing basketball forever, because of the subsequent teasing. So while competition with women can increase the overall performance of men, the social consequences of losing can be devastating. Note that the boy described by Shakib and Dunbar did not attribute his friend giving up basketball to the girl beating him, but to his friends' response.
It appears that competition with women can encourage men to work harder to meet their potential. But is the benefit of that work worth the social cost of the disdain for women and those they defeat?
Occasionally I have moments that illustrate the difference between my perceived gender and my socialized reactions very clearly. The most recent was at a party. A young man was demonstrating some martial arts holds that he taught his students, and how easily they could make someone bend. The other men at the party were lining up to have this hold demonstrated, and one by one, they found themselves bent back at a disadvantage. I thought this looked interesting, and took a turn myself. When I felt the pressure on my wrist, I followed through with the non-verbal "hint" and bent back, as if I were following the lead of a dancer.
The profound effect this had on the man demonstrating the hold, and the other men watching, was remarkable. "Wow," the demonstrator said, "you went right down." I had not realized that the point of the experiment was to see who could resist the hold the best. I had not fought the hold, and my failure to do so obviously made everyone a little uncomfortable. My own failure to treat it like a competition seemed to turn the entire exercise into something else, something different from the posturing they had been participating in. The conversation awkwardly changed, and no one asked any more questions about martial arts in my presence that evening.