That last “if you know the other person cooperated” is unnecessary, in a True Prisoner’s Dilemma each player prefers defecting in any circumstance.
Not quite: e.g. If you’re playing True Prisoner’s Dilemma against a copy of yourself, you prefer cooperating, because you know your choice and your copy’s choice will be identical, but you don’t know what the choice will be before you actually make it.
If you don’t know for sure that they’ll be identical, but there’s some other logical connection that will e.g. make it 99% certain they’ll be identical. (e.g. your copies were not created at that particular moment, but a month ago, and were allowed to read different random books in the meantime), then one would argue you’re still better off preferring cooperation.
Given the context, I was assuming the scenario being discussed was one where the two players’ decisions are independent, and where no one expects they may be playing against themselves.
You’re right that the game changes if a player thinks that their choice influences (or, arguably, predicts) their opponent’s choice.
Not quite: e.g. If you’re playing True Prisoner’s Dilemma against a copy of yourself, you prefer cooperating, because you know your choice and your copy’s choice will be identical, but you don’t know what the choice will be before you actually make it.
If you don’t know for sure that they’ll be identical, but there’s some other logical connection that will e.g. make it 99% certain they’ll be identical. (e.g. your copies were not created at that particular moment, but a month ago, and were allowed to read different random books in the meantime), then one would argue you’re still better off preferring cooperation.
Given the context, I was assuming the scenario being discussed was one where the two players’ decisions are independent, and where no one expects they may be playing against themselves.
You’re right that the game changes if a player thinks that their choice influences (or, arguably, predicts) their opponent’s choice.