You just described the reasoning you would go through when making a decision. That would seem to be answer enough to demonstrate that this is a decision problem.
I don't see how this is a decision problem at all.
Interesting.
It seems to me that if my reasoning tells me that no matter what decision I make, the same thing happens, that isn't evidence that I have a decision problem.
But perhaps I just don't understand what a decision problem is.
This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.
Here's a diagram: