We've talked about some aspects of Nash's game theory, like - if everyone if being a leader, you should be a follower, etc. Another key view of Nash's theory is to make your own moves based on your predictions of how others will move. The more predictable others are, the better able you are to choose what you will do.
In fact, if your move does not affect their strategy, they won't change their mind, even if they know what you are going to do.
Example - Jenna and Heidi hate Rob. However, they also want to win the million dollars. Therefore, they could see the benefit of allying with him even now. Even though they expect him to try to screw them as soon as he can.
In order to invoke Nash's theory, you have to know what drives the competitors. Example, Jenna and Heidi want to win the $$, but not (at least so far) at the expense of betraying close friends.
Rob wants to win, and will betray anyone.
Butch seems to feel loyalty is the most important thing.
Matt I'm not sure about yet, but I think honesty will prove his underlying motivation, along with the $$.
This brings us to Christy. Unfortunately, Christy was openly ambiguous about her goals at this point. She told us in the confessionals, and she told the other players, she was not sure whether it was more important for her to win the money, or to screw the poeple who had been mean to her. This made her an unpredictable player, and is the reason why they had to get rid of her. No one could plan their own moves with any degree of certainty when a wild card like that is around.
Once everyone's motivation is out on the line for everyone to see, all the players (according to Nash) choose their moves based on what will be best for them. If you don't know the other players' motivation, you can't plan your own move.