Recent experimental results indicate that women do not like competitive environments as much as men do. Another literature is interested in the effect of social identity on economic behaviors. This paper investigates in the lab the impact of social identity on men and women's willingness to compete both individually and as part of a team. To this aim, participants from the Identity sessions had to go through group identity building activities in the lab while participants from the Benchmark sessions did not. The main result is that men are only willing to enter a team competition with a teammate of unknown ability if they share a common group identity with him or her. This change of behavior seems to be caused by high-performing men who are less reluctant to be matched with a possibly less able participant when he or she belongs to his group. On the other hand, group identity does not seem to induce women to take actions more in the interest of the group they belong to.