To investigate whether men and women respond differently to competition and whether this response depends on the gender mix of the group, the author examines outcomes of the Mellon Foundation's Graduate Education Initiative, a competitive fellowship program instituted in 1991 that was aimed at increasing graduation rates and decreasing time to degree. Men's performance, as measured by time to candidacy, increased 10% in response to the program, with the largest gains for men in departments with the highest proportions of female students. Women did not increase performance, on average, but the response of women did differ greatly depending on the gender mix of their peers, with a more positive response when a larger fraction of the group was female. These results suggest that when devising incentive schemes, policy-makers may need to be mindful of an inherent tradeoff between increasing aggregate outcomes through the use of competition and achieving gender equity.