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We conducted a field experiment involving 720 Italian undergraduate students to investigate the existence of gender differences in performance in competitive settings and whether performance is affected by one's opponent gender. The experimental design was aimed at disentangling gender differences in taste for competition from other differences in psychological attitudes, such as self-confidence and risk aversion. Students were invited to undertake a midterm exam under a tournament scheme having as a prize some bonus points to add to the final grade. Students competed in pairs of equal predicted ability but different gender composition. We find that females are as likely as males to take part in the competition and to obtain a good performance. The gender of one's competitor does not play any role in shaping students' behavior. Men and women perform similarly both in the competitive and in the non-competitive environment.