I'd never heard of tit for tat, and it sounds interesting. My only knowledge of game theory comes from trying to wrap my head around the attempts being made at finding optimal poker strategy. I like the concept that cooperation can be the most successful strategy when it is a shared strategy. Though one thing stuck out at me when I was reading about tit for tat just now. The word "opponent" kept cropping up. That's a very specific social relationship; one which I would not want to consider the foundation of any ideal society. But I found your use of the phrase "game theory in nature" very interesting. I think you might enjoy the book "Mutual Aid," by Kropotkin. He is my favorite anarchist writer, and his studies in biology found that cooperation had evolutionary advantages.
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I haven't yet read any Kropotkin, but I plan to. Thanks for the recommendation. Game theorists use competitive language, but that doesn't mean it can't be mutually beneficial in a cooperative sense. I recently read the Selfish Gene, and it's interesting to me how much evolutionary stable strategies involve cooperation and tit for tat game theory. In many ways, tit for tat (as far as I understand it) is similar to the NAP. It's not pacifism, but it also won't initiate negatively. It rewards cooperation.