"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 is best and I think it said "take action x such that, if you do x, and everyone after 15:42 UTC Mar 24, 2023 knew that you'd do x, you'll do as well as possible.". So what deserves to be called "rational" may be to do what the person you wish you were would do.