In the final round of the game, called "Split or Steal," two contestants play a one-shot Prisoner's Dilemma -- technically, it's a variant -- choosing to either cooperate (and split a jackpot) or defect (and try to steal it). If one steals and the other splits, the stealer gets the whole jackpot. And, of course, if both contestants steal then both end up with nothing. There are lots of videos from the show on YouTube. (There are even two papers that analyze data from the game.) The videos are interesting to watch, not just to see how players cooperate and defect, but to watch their conversation beforehand and their reactions afterwards. I wrote a few paragraphs about this game for Liars and Outliers, but I ended up deleting them.
This is the weirdest, most surreal round of "Split or Steal" I have ever seen. The more I think about the psychology of it, the more interesting it is. I'll save my comments for the comments, because I want you to watch it before I say more. Really.
In 2003 I went to a TV show here in Brazil called "Sete e Meio", on SBT, that was exactly like this. My strategy was exactly the one that Bruce mentions, but unfortunately I never got to the final round — I got myself some money, though. :)