Yep, this all seems correct; the player does not have enough degrees of freedom to prevent there from being a fixpoint, and it is possible to prove for all interpretations that no strategy does better than tying with the simple one-box strategy. But I feel, very strongly, that allowing this particular kind of ambiguity into decision theory problems is a reliably losing move. That road leads only to confusion, and that particular mistake is responsible for many (possibly most) previous failures to figure out decision theory.
Yep, this all seems correct; the player does not have enough degrees of freedom to prevent there from being a fixpoint, and it is possible to prove for all interpretations that no strategy does better than tying with the simple one-box strategy. But I feel, very strongly, that allowing this particular kind of ambiguity into decision theory problems is a reliably losing move. That road leads only to confusion, and that particular mistake is responsible for many (possibly most) previous failures to figure out decision theory.