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orthonormal comments on Decision Theories: A Semi-Formal Analysis, Part II - Less Wrong
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Well, the substitutions are specifically to turn a circularity into a case of having x on both sides of some equation. We might be talking about different things. The failure mode is benign; you arrive at x=x .
edit: ahh, another thing. If you have source of randomness, you need to consider the solution with, and without, the substitution, as you can make substitution invalid by employing the random number generator. The substitution of the nonrandom part of strategy can still be useful though. Maybe that's what you had in mind?
Err, I'm not sure what you mean here. In the CDT algorithm, if it deduces that Y employs a particular mixed strategy, then it can calculate the expected value of each action against that mixed strategy.
(For complete simplicity, though, starting next post I'm going to assume that there's at least one pure Nash equilibrium option in G. If it doesn't start with one, we can treat a mixed equilibrium as x{n+1} and y{m+1}, and fill in the new row and column of the matrix with the right expected values.)