[FakeComments]

That doesn’t require infinite length, just indeterminate length and more than a single round (on average, or with certain rate).

And I’m not sure that it doesn’t apply to the case where:

A) You can’t determine when the game will end, and

B) There’s very often several rounds.

That seems to cover “society”, in a broad sense.

[philipov]

Yes, that's what I'm saying. Whether it applies to society or not depends on how often you have repeat interactions with the same person. For example, in a big city where you can expect to never run into someone again, I would expect people to favor Betray over Cooperate. Whereas, in a small village where you can't escape the people around you, I would expect people to favor Cooperate.