I guess I just like game theory. “Alice chooses a box and Bob predicts her action” can be viewed as a game with Alice and Bob as players, or with only Alice as player and Bob as the shape of the game tree, but in any case it seems that option (2) from the post leads to games where solutions/equilibria always exist, while (1) doesn’t. Also see my other comment about amnesia, it’s basically the same argument. It’s fine if it’s not a strong argument for you.
I guess I just like game theory. “Alice chooses a box and Bob predicts her action” can be viewed as a game with Alice and Bob as players, or with only Alice as player and Bob as the shape of the game tree, but in any case it seems that option (2) from the post leads to games where solutions/equilibria always exist, while (1) doesn’t. Also see my other comment about amnesia, it’s basically the same argument. It’s fine if it’s not a strong argument for you.