"Obey so they don't carry out their threat." may be prescribed by classical decision theory, but I wouldn't call it rational when it's bad for you to be known to do it. I just asked classical decision theory what decision theory to pick and I think it said "take action x such that, if you do x, and everyone had known since 15:53 UTC Mar 24, 2023 that you'd do x, you'd have done as well as possible.". So what deserves to be called "rational" may be to do what the person you wish you'd always been would do.
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