Evolutionary psychologists ponder altruism. They wonder why anybody behaves in a manner that appears less than self-interested. They speculate that charity is a charade; it is not benevolent but serves another purpose.
Rather than simply cheating -- trying to gain from another's cooperative behaviour without behaving cooperatively yourself -- lying adds another way of operating. By misleading the other individual, one can trick that individual into cooperating.
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.