The phrase that makes me roll my eyes is "survival of the fittest." That's not what natural selection is. It's a gradual increase in variation with the death of the unfit. An organism doesn't have to be "the fittest," it just has to find an unoccupied niche. Thus the various "strategies" different organisms will take for survival -- be it cooperation, selfishness, or some combination of the two -- will vary depending on the organism.
Ants are pretty cooperative. Big cats are pretty selfish and territorial. But wild/feral horses are an interesting combination of the two. They have herds of mares with a few stallions. The stallions attack any other stallion that comes near and once a young stallion grows to a certain age they banish it from the herd. The stallions act pretty selfishly while the mares act rather cooperatively (however, they have a hierarchy so there's some selfishness involved, too).
I think the problem is trying to theorize a formula for understanding the behavior of organisms, or a most successful behavior, in general. There's just way too much diversity in nature for something like game theory to cover all its ground. Perhaps it works when you pigeon-hole it into capitalist economics, but I don't think it's a very comprehensive theory for explaining how animals do or ought to act.