Daniel Balliet, Norman Li, Shane Macfarlan and Mark Van Vugt did a meta-analysis of 272 research findings over the past 50 years exploring men and women in cooperative settings.
This paper was published in the November, 2011 issue of Psychological Bulletin. In a meta-analysis, researchers analyze the data from many studies conducted over a long period of time and try to extract patterns that might not be evident from any individual study.
For example, many studies have explored a particular setting called the “Prisoner's Dilemma.”
On average, men and women are about equally likely to cooperate in games like this. However, the pattern of cooperation differs:
Men are most likely to cooperate when they are playing against other men. Women are much less likely to cooperate when playing against other women. When the game involves a mixed-sex pair, then women are much more likely to cooperate than men.
When the game is played repeatedly, men are more likely to cooperate than women over time. Essentially, in games like this women are more likely than men to punish someone who rats on them.
Overall, there is one other finding of importance here. All of the differences that the authors observed were rather small. That is, while gender does influence how likely people are to cooperate to some degree, it is hardly the most important factor.
Practically speaking, then, if you are trying to create an environment in which people are going to cooperate, you are probably better off fostering an environment of team unity and trust than you are focusing on the gender balance of the group.