That’s only because you’re not just adding an option, you’re changing the choice you already have. You’re not going from X to a choice between X and Y, but rather from X to a choice between X+(B knows A prefers this choice to the other) and Y+(B knows A prefers this choice to the other). This has nothing to do with there being another agent about, it’s just the fact that you’re changing the options available at the same time as you add extra ones.
EDIT: As a general principle, there shouldn’t be any results that hold except when there are other agents about, because other agents are just part of the universe.
That’s only because you’re not just adding an option, you’re changing the choice you already have. You’re not going from X to a choice between X and Y, but rather from X to a choice between X+(B knows A prefers this choice to the other) and Y+(B knows A prefers this choice to the other). This has nothing to do with there being another agent about, it’s just the fact that you’re changing the options available at the same time as you add extra ones.
EDIT: As a general principle, there shouldn’t be any results that hold except when there are other agents about, because other agents are just part of the universe.
Aha. Thanks for the correction.