I think you’d still just choose A at the start here if you’re considering what will happen ahead of time and reasoning via backwards induction on behalf of the necessary people. (Assuming C is worse than A for the original necessary people.)
If you don’t use backwards induction, you’re going to run into a lot of suboptimal behaviour in sequential choice problems, even if you satisfy expected utility theory axioms in one-shot choices.
I think you’d still just choose A at the start here if you’re considering what will happen ahead of time and reasoning via backwards induction on behalf of the necessary people. (Assuming C is worse than A for the original necessary people.)
If you don’t use backwards induction, you’re going to run into a lot of suboptimal behaviour in sequential choice problems, even if you satisfy expected utility theory axioms in one-shot choices.