We invariably put self interest over cooperation.
Not necessarily. Psychological studies show primates, including chimps and humans, are far more "successful" (become leaders, get more mating opportunities, get fed) when they cooperate with one-another. Animals (and by extension, people) who act in a selfish manner and refuse to cooperate with the rest of the group most often find themselves to be outcasts and end up far less successful. To make a long story short (too late), for me to get mine I have to make sure you get yours too.