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?
It's irrelevant if you are dealing with robots or people who aren't spiteful.
But some people would actually kick themselves in the nuts just to watch you get hit by a truck. People do it all the time. Just pay attention to politics. A huge segment of the population is motivated by spite, envy, and jealousy, and would make themselves suffer as long as people they consider undeserving suffer more. It's quite sick.