If there's a decision to be made, there's a game-theoretic model of that decision. It's not always easy to compute, but it exists. Things like the Prisoner's Dilemma are the result of game theory analysis.
In the video above, Ibrahim's decision about whether to choose "Split" or "Steal" is morphed into a meta-game about whether or not he wants to get any money at all. While I relish this approach, it looks like it can only really be used once on this show because future participants will have to doubt the veracity of the claim "I'm going to steal, so just choose split."
Amazing Round of "Split or Steal" at Schneier on Security for a longer discussion.
Game show game theory at tutor2u for a Game Theory analysis of the game.
The Predictioneer's Game for a site that discusses how game theory can be applied to make predictions about future political behavior.