Seconding jimrandomh: you seem to be talking about issues that don't matter to decision theory very much. Let me reframe.

My own interest in the topic was sparked by Eliezer's remark about "AIs that know each other's source code". As far as I understand, his interest in decision theory isn't purely academic, it's supposed to be applied to building an AI. So the simplest possible approach is to try "solving decision theory" for deterministic programs that are dropped into various weird setups. It's not even necessary to explicitly disallow randomization: the predictor can give you a pony if it can prove you cooperate, and no pony otherwise. This way it's in your interest in some situations to be provably cooperative.

Now, if you're an AI that can modify your own source code, you will self-modify to become "provably cooperative" in precisely those situations where the payoff structure makes it beneficial. (And correspondingly "credibly threatening" in those situations that call for credible threats, I guess.) Classifying such situations, and mechanical ways of reasoning about them, is the whole point of our decision theory studies. Of course no one can prohibit you from randomizing in adversarial situations, e.g. if you assign a higher utility to proving Omega wrong than to getting a pony.