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.
Sometimes I see new ideas that, without offering any new information, offers a new perspective on old information, and a new way of thinking about an old problem. So it is with this lecture and the prisoner's dilemma.
Now, I worked a lot with the prisoners dilemma, with superrationality, negotiations, fairness, retaliation, Rawlsian veils of ignorance, etc. I've studied the problem, and its possible resolutions, extensively. But the perspective of that lecture was refreshing and new to me:
The prisoner's dilemma is resolved only when the off-diagonal outcomes of the dilemma are known to be impossible.
The "off-diagonal outcomes" are the "(Defect, Cooperate)" and the "(Cooperate, Defect)" squares where one person walks away with all the benefit and the other has none:
Facing an identical (or near identical) copy of yourself? Then the off-diagonal outcomes are impossible, because you're going to choose the same thing. Facing Tit-for-tat in an iterated prisoner's dilemma? Well, the off-diagonal squares cannot be reached consistently. Is the other prisoner a Mafia don? Then the off-diagonal outcomes don't exist as written: there's a hidden negative term (you being horribly murdered) that isn't taken into account in that matrix. Various agents with open code are essentially publicly declaring the conditions under which they will not reach for the off-diagonal. The point of many contracts and agreements is to make the off-diagonal outcome impossible or expensive.
As I said, nothing fundamentally new, but I find the perspective interesting. To my mind, it suggests that when resolving the prisoner's dilemma with probabilistic outcomes allowed, I should be thinking "blocking off possible outcomes", rather than "reaching agreement".