Muriel Niederle (Stanford University, Department of Economics) & Lise Vesterlund (University of Pittsburgh, Department of Economics) have posted Do Women Shy Away From Competition? Do Men Compete Too Much? on the NBER web site.  Here is part of the description from the February 2006 NBER Digest:

The proportion of women in highly paid executive positions and in the professorial ranks of academic science and engineering is low relative to the proportion of women in the labor force. A number of explanations for this difference have been advanced. If women do not enjoy the kind of work involved in high profile managerial positions or scientific careers, or if the long working hours required in these careers conflict with the ability to raise children, then women may avoid them. Because women on the whole are less likely to be in the highest scoring group on tests of mathematical achievement, they also may be less likely as a group to be successful in competitive science and engineering positions that reward mathematical talent. Some also have argued that past discrimination has kept women from highly paid executive and academic positions, and that women subsequently avoided those careers simply to escape discrimination.

Muriel Niederle and Lise Vesterlund consider another possibility, that women as a group dislike competition more than men, even if they are of the same ability. If women seek to avoid competition, then they may be less successful in obtaining promotions and more lucrative jobs.