You can play all sort of mind games to make her believe that you won't take an "unfair" offer, but the formulation states that she'll offer you $10 nevertheless.  Your option (or not) to communicate before she makes her call only matters as far as that would affect your decision.

I mean, would you accept more or less money if you had a chance to state your position first?  If you swore you wouldn't take anything but half and she offered $10, would you be any more or less likely to accept it, in relation to the case where you didn't get a chance to talk before her offer?

If not, then all this talk about mind games is irrelevant to the question, isn't it?