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Vladimir_Nesov comments on Stupid Questions Open Thread Round 3 - Less Wrong
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It's not possible to coordinate in general against arbitrary opponents, like it's impossible to predict what an arbitrary program does, but it's advantageous for players to eventually coordinate their decisions (on some meta-level of precommitment). On one hand, players want to set prices their way, but on the other they want to close the trade eventually, and this tradeoff keeps the outcome from both extremes ("unfair" prices and impossibility of trade). Players have an incentive to setup some kind of Loebian cooperation (as in these posts), which stops the go-meta regress, although each will try to set the point where cooperation happens in their favor.
I was thinking rather of Halting Problem - like impossibility, along with rock-paper-skissors situation that prevents declaring any one strategy, even the cooperative, as the 'best'.
If difficulty of selecting and implementing a strategy is part of the tradeoff (so that more complicated strategies count as "worse" because of their difficulty, even if they promise an otherwise superior outcome), maybe there are "best" strategies in some sense, like there is a biggest natural number that you can actually write down in 30 seconds. (Such things would of course have the character of particular decisions, not of decision theory.)
There is not a biggest natural number that you can actually write down in thirty seconds -- that's equivalent to Berry's paradox.
Huh? Just start writing. The rule wasn't "the number you can define in 30 seconds", but simply "the number you can write down in 30 seconds". Like the number of strawberries you can eat in 30 seconds, no paradox there!
I was reading "write down" more generally than "write down each digit of in base ten," but I guess that's not how you meant it.
Hmm if it was a programming contest I would expect non-transitive 'betterness'.
Given a fixed state of knowledge about possible opponents and finite number of feasible options for your decision, there will be maximal decisions, even if in an iterated contest the players could cycle their decisions against updated opponents indefinitely.