Honest question, given the tens of thousands of years of humans cooperating to form groups of increasingly large size and interdependence, what makes you think there is more competition than cooperation happening?
In caveman times you were _far_ more likely to be killed via violent encounter, starve to death, or die from minor accidents or infections, etc. The average life expectancy was about 20 years, and a painful death was highly likely. And while you can't cooperate for a mate, there is no shortage of mate's to go around and likely millions of suitable matches for any particular person today. So however far from utopia we might be now, we are certainly _far_ closer than caveman times.