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Perplexed comments on Timeless Decision Theory: Problems I Can't Solve - Less Wrong
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Comments (153)
Strategies are probability (density) functions over choices. Behaviors are the choices themselves. Proving that two strategies are identical (by symmetry, say) doesn't license you to assume that the behaviors are the same. And it is behaviors you seem to need here. Two random variables over the same PDF are not equal.
Seldin got a Nobel for re-introducing time into game theory (with the concept of subgame perfect equilibrium as a refinement of Nash equilibrium). I think he deserved the prize. If you think that you can overturn Seldin's work with your TDT, then I say "To hell with a PhD. Write it up and go straight to Stockholm."
After looking at this: http://lesswrong.com/lw/vp/worse_than_random/
...I figure Yudkowsky will not be able to swallow this first sentence - without indigestion.
In this case, I can only conclude that you haven't read thoroughly enough.
I think EY's restriction to "cryptographic adversaries" is needlessly specific; any adversary (or other player) will do.
Of course, this is still not really relevant to the original point, as, well, when is there reason to play a mixed strategy in Prisoner's Dilemma?
Even if your strategy is (1,0) or (0,1) on (C,D), isn't that a probability distribution? It might not be valuable to express it that way for this instance, but you do get the benefits that if you ever do want a random strategy you just change your numbers around instead of having to develop a framework to deal with it.
The rule in question is concerned with improving on randomness. It may be tricky to improve on randomness by very much if, say, you face a highly-intelligent opponent playing the matching pennies game. However, it is usually fairly simple to equal it - even when facing a smarter, crpytography-savvy opponent - just use a secure RNG with a reasonably secure seed.
...unless the resulting strategies are unmixed, as will usually be the case with Prisoner's Dilemma?