Unless otherwise stated, the games theory game of Prisoner's Dilemma takes place as the only event in the hypothetical universe; in this example, prior communication and credible precommitment are not permitted.
Instead of generating a strategy to use against a copy of yourself, consider what the best strategy would be against the optimized player who knows what your strategy is.
TDT permits acting as though one had precommitted, the result being that one never wishes one's opportunities to precommit were different. Consider a perfectly reasoning person and a perfectly reasoning Omega with the added ability to know what the person's move will be before making its own move (and not mind-reading; only knowing the move).
If the human knows TDT is optimal, then he knows Omega will use it; if the human knows that TDT would make the true but non-credible precommittment, then the human knows that Omega has chosen the optimal precommitment.
If the ideal silent precommitment strategy is the diagonal, then we get C-C as the result. If any other precommitment is ideal, then Omega would do no worse than 3 points using it against a perfectly rational non-precog.
If the human is a cooperate-bot, then the ideal strategy is to defect. Therefore committing to the diagonal is suboptimal, because it results in 3 instead of 5 points in that one case. However, the human here is either going to cooperate or defect without regard to Omega's actual strategy (only the ideal strategy), meaning that the human is choosing between 0 and 1 if the ideal strategy is defectbot.
Either there's a potential precommit that I haven't considered, TDT is not optimal in this context, or I've missed something else. Evidence that I've missed something would be really nice.
Either you haven't read this, and are not talking about TDT as I know it, or I don't understand you at all.
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".