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Decius comments on Other prespective on resolving the Prisoner's dilemma - Less Wrong
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What if you are playing with someone and their decision on the current round does not affect your decision in the current round?
If you are known to cooperate because it means that your opponent (who is defined as 'similar to yourself'), then your opponent knows he is choosing between 3 points and 5 points. Being like you, he chooses 3 points.
If you are playing against someone whose decision you determine, (or influence) then you choose the square; if the nature of your control prevents you from choosing 5 or 0 (or makes those very unlikely) points but allows you to choose 3 or 1 (or make one of those very likely), choose 3. However, there only one player in that game.
I don't care which way the causal chain points. All I care about is if the decisions correlate.
Also, I'm not sure of most of what you're saying.
Given the choice between 0 points and 1 point, you would prefer 1 point; given the choice between 3 points and 5 points, you would prefer 3 points. (Consider the case where you are playing a cooperatebot; the choice which correlates is cooperation; against a defectbot, the choice which correlates is defection. There are no other strategies in single PD without the ability to communicate beforehand.)
Why would you prefer three points to five points? Aren't points just a way of specifying utility? Five points is better than three points by definition.
Right- which means defectbot is the optimal strategy. However, when playing against someone who is defined to be using the same strategy as you, you get more points by using the other strategy.
It should not be the case that two players independently using the optimal option would score more if the optimal option were different.