TheOtherDave comments on Decision Theories: A Less Wrong Primer - Less Wrong
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OK, ignore those examples for a second, and ignore the word "advanced."
The OP is drawing a distinction between CDT, which he claims fails in situations where competing agents can predict one another's behavior to varying degrees, and other decision theories, which don't fail. If he's wrong in that claim, then articulating why would be helpful.
If, instead, he's right in that claim, then I don't see what's useless about theories that don't fail in that situation. At least, it certainly seems to me that competing agents predicting one another's behavior is something that happens all the time in the real world. Does it not seem that way to you?
But the basic assumption of standard game theory, which I presume he means to include in CDT, is that the agents can predict each other's behavior -- it is assumed that each will make the best move they possibly can.
I don't think that predicting behavior is the fundamental distinction here. Game theory is all about dealing with intelligent actors who are trying to anticipate your own choices. That's why the Nash equilibrium is generally a probabilistic strategy -- to make your move unpredictable.
I'm not sure that equating "CDT" with "standard game theory" as you reference it here is preserving the OP's point.