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Decius comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong
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For the Unlimited Swap game, are you implicitly assuming that the time spent swapping back and forth has some small negative utility?
No. There's no utility lost. But if you both wait forever, no-one gets any utility.
Can you define "forever" in this scenario? I thought it was infinite, so there is no such thing.
You can communicate any finite number instantly. Or, in the second version, you can't, but you are compensated for any time, but you receive the utility when you halt.