Are iterated Prisoner's Dilemmas impossible?

When we get to the last shot of our iterated Prisoner's Dilemma, it will be like a one-shot Prisoner's Dilemma again. There will be no prospect of future cooperation after the last instance of interaction, after all. So, one might think, the last one shouldn't be counted as part of the iterated set.

This would mean that the second-to-last one is the last one. But if the second-to-last interaction should be treated as the last one, then the second-to-last interaction should be regarded as a one-shot Prisoner's Dilemma just as the last one is. So the second-to-last interaction shouldn't count in the iterated set either.

Now we move on to the third-to-last one ... You see where this is going. The set of iterated Prisoner's Dilemmas seems to shrink until we're back to a simple one-shot case! We should be careful not to take this argument in the wrong way.

There's a puzzle here: how could there be an iterated Prisoner's Dilemma? But the puzzle might make us lose sight of what we're after. ... more.

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