Gender differences in paid performance under competition have been found in many laboratory-based experiments, and it has been suggested that these may arise because men and women respond differently to psychological pressure in competitive environments. To explore this further, we conducted a laboratory experiment comprising 444 subjects, and measured gender differences in performance in four distinct competitive situations. These were as follows: (i) the standard tournament game where the subject competes with three other individuals and the winner takes all; (ii) an anonymized competition in which an individual competes against an imposed production target and is paid only if s/he exceeds it; (iii) a 'personified' competition where an individual competes against a target based on the previous performance of one anonymised person of unknown gender; and (iv) a 'gendered' competition where an individual competes against a target based on the previous performance of one anonymised person whose gender is known. We found that only men respond to pressure differently in each situation; women responded the same to pressure no matter the situation. Moreover, the personified target caused men to increase performance more than under an anonymized target and, when the gender of the person associated with the target was revealed, men worked even harder to outperform a woman but strived only to equal the target set by a male.