Wired has an article about game design and game theory in Survivor:

While tweaking Survivor, he closely studied John Nash’s game theory in order to better engineer the hysteria and emotional blowouts of each season’s finale.

“What Nash’s theory predicts is that whenever you have a group of people competing, they collude to squeeze one guy out, again and again, until there’s only two guys left,” Burnett notes. “Yet when there are only two of us left, we’re surprised when one of us fucks each other over. That’s the fun part. It surprised John Nash himself, but it happens every time.”