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Qiaochu_Yuan comments on Bayesians vs. Barbarians - Less Wrong
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I know this post is long, long dead but:
Isn't this a logical impossibility? To have knowledge is to contain it in your source code, so A is contained in B, and B is contained in A...
Alternatively, I'm considering all the strategies I could use, based on looking at my opponent's strategy, and one of them is "Cooperate only if the opponent, when playing against himself, would defect."
"Common knowledge of each other's rationality" doesn't seem to help. Knowing I use TDT doesn't give someone the ability to make the same computation I do, and so engage TDT. They have to actually look into my brain, which means they need a bigger brain, which means I can't look into their brain. If I meet one of your perfectly rational agents who cooperates on true prisoners dilemma, I'm going to defect. And win. Rationalists should win.
The idea is that A and B are passed each other's source code as input (and know their own source code thanks to that theorem that guarantees that Turing machines have access to their own source code WLOG, which I think DanielLC's comment proves). There's no reason you can't do this, although you won't be able to deduce whether your opponent halts and so forth.
Your opponent might not halt when given himself as input.