I use the introduction of a competitive fellowship program for graduate students to test whether men and women respond differently to competition and whether this response depends on the gender mix of the group. Men experienced a 10% increase in performance in response to the program, with the largest gains for men in departments with the most 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. (Contains 7 tables and 5 footnotes.)