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Which is the entire point. If either player tried to play in a way that would result in the best result for everyone, they would get taken advantage of by people just being selfish. So yeah, not a very convincing argument for why people being selfish yields the best results for everyone.
Being selfish without arbitrary restrictions in the game does result in the best result. Because it's in everyone's self interest to cooperate with people who are cooperating.
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And it's still significantly worse than cooperation every round.
Not really, there are costs to enforce cooperation every round. And by doing tit-for-tat, it enforces those costs by taking some hit yourself, then teaching them for not cooperating. If you are playing with someone who will not cooperate no matter what, you are better off defecting.
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I agree that the prisoner's dilemma is too restrictive, but look at the rest of what you're saying. You're saying that people are wired in a way that makes them not act in their best interest, while trying to defend the claim that people acting in their best interest yields the best results for society.
Assuming that you really want to say something along the lines of "people looking out for their best interested, but with the restrictions naturally put into place by our biology, yields the best results for society," then I would ask why you believe our natural mechanisms are better than anything else we could put in place on top of that, and also why you think natural mechanisms work well in today's world.
Ostracism and feelings of guilt works in some contexts, but when people aren't living in small societies where everyone knows one another, and many of our interactions with people are so impersonal, I wouldn't expect our natural tendency to cooperate to be perfectly suited for our conditions.
No, I'm saying that it results in their best interest. Cooperation in this case *is* self-interested. They try to force cooperation precisely because it's good for them in the long run.
But I do agree that what most people considered self-interested isn't what most people are wired to be rewarded for. But that just means that feeling good for cooperating or punishing evil people are just things that need to be accounted for in self-interest.