Of course it would be nice if you could negotiate in things like the Prisoner's dilemma - that's pretty much why you can't. If you could find a common-ish real life analogue of the situation you're thinking about, though, I'd probably give a far less snippy answer :P

As for regretting your choice when the stakes are huge - I think "just dealing with it" is an interesting skill that us humans have, But more seriously, if ALL mistakes are scaled up it shouldn't make any difference to the best option, nor should it make you feel more guilty if you do your best and fail.

but we zoom out and observe that, unbeknownst to you, Omega has abducted your fellow LW reader and another paperclip maximizer from that same dimension, and is making them play PD. But this time their payoff matrix is like this:

Omega like entities are assumed not to be misleading us and we are assumed to have absolute faith in that fact. This means that while we may not know the specifics of what Omega is doing to change the behaviour of our opponent we will know that that kind of thing is part of the game. Since I certainly don't have enough information about the kinds of things that may change the clipper nor the processing ability to calculate likely outcomes from such interference (including, for example, predicting LW readers) it is obviously necessary for me to defect.

You are also told some specifics about the algorithm that the alien uses to reach its decision, and likewise told that alien is told about as much about you. At this point I don't want to nail the algorithm the opposing alien uses down to one specific. We're looking for a method that wins when summing up all these possibilities. Next, especially, we're looking at the group of AI's that are capable of superrationality, since against other's the game is trivial.

Had the decision not been determined elsewhere this would be insufficient. I need to know what has been told to the clipper about me and what I have been told about the me to the clipper. "Capable of superrationality" is not especially meaningful until I am told exactly what that means in the instance.

TL;DR Entities chasing each other in spirals through their minds may eventually meet and shake hands, but logic alone does NOT give you the ability to do this. You need access to each other's source code.

It seems to me what "superrationality" is grasping towards is the idea that if both players can predict each other's actions, it provides pragmactic grounds for cooperation. All the other crap, (the skewed payoff matrix, hofstader's "sufficiently logical" terminology, even the connotations of the word "superrationality" itself) are red herrings.

This all hinges on the idea that your decision CAN affect their decision, through their mental emulation of you, and vice versa. If it's one-sided, we have newcomb's problem, except it collapses to a normal prisoner's dilemma, since although omega knows if you'll cooperate, you have no way of knowing if omega will cooperate, and thus he has no incentive to base his behavior on your decision, even though he knows it. He's better off always defecting.

This is a point that a lot of people here seem to get confused about. They think "but, if I could predict omega's actions, he'd have an incentive to conditionally cooperate, and so I'D have an incentive to cooperate, and we'd cooperate, and that'd be a better outcome, ergo that must be more rational, and omega is rational so he'll act in a way I can predict, and specifically he'll conditionally cooperate!!1"

But I think this is wrong. The fact that the world would be a better place if you could predict omega's actions, (and the fact that omega knows this) doesn't give omega the power to make you capable of predicting his actions, any more than it gives him the power to make your mom capable of predicting his actions, or to make a ladybug capable of predicting his actions, or another superintelligence capable of predicting his actions (although possibly it could to start with). He's in another room.

The fact that he knows what you're going to do means there's already been some information leakage, since even a superintelligence can't extrapolate from the fact that your name is jeff what decision you'll make in a complicated game. He apparently knows quite a bit about you.

And if you knew ENOUGH about him, including his superhuman knowledge of yourself, and were smart enough to analyze the data (good luck), you'd be able to predict his actions too. But it seems disingenuous to even call that the prisoner's dilemma.

if they take into account how much the other cares about those results, using some unknown method, they just might be able to systematically perform better

Systematically perform better, but in this specific situation perform worse? That doesn't sound like a winning strategy on a one-shot dilemma. And the parenthetical patch doesn't seem to fix this problem: if the payoffs are randomly assigned in this one-shot case, and you get the short end of the stick - well, you know you aren't going to get another chance, because it's a one-shot case. Good luck trying to counterfactually mug the player here.

"You are also told some specifics about the algorithm that the alien uses to reach its decision, and likewise told that alien is told about as much about you."

If I know enough to see that my decision doesn't affect the alien's, I defect. If I don't know enough, I consider that the alien might know what my own algorithm is. Therefore I decide to cooperate if I think the alien will cooperate. I assume the alien knows this and that he knows that I know. Therefore I assume that the alien will cooperate because he thinks this will cause me to cooperate based on his knowledge of my thought processes (and CC is preferable to DD). Following the algorithm laid out above, I cooperate.

This is still just superrationality, though a little more advanced than usual. I have incomplete knowledge about my opponent's thought processes, I assume the rest will be similar to mine, consequently I choose the optimum symmetric strategy and hope he does the same.