Apr 20 2012
UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior!
In my original “Golden Balls” blog post (see below), written almost three years ago after I saw a clip of the finale in an episode of the British game show, Golden Balls, I analyzed the actions of Sarah and Steve, who had to decide whether they would split or steal a jackpot of 100,000 British pounds. The contestants had one minute to try to convince one another that they would split the money; but when it came down to it Sarah stole and Steve split, meaning Sarah got to keep the whole jackpot and Steve went home with nothing.
In that original post, I proposed that Steve's best chances for going home with any money would have been “for him to use the one minute of discussion time to convince Sarah that he would choose SPLIT, yet be willing to go home with something LESS THAN $50,000 and accept that Sarah was going to choose STEAL. He could have threatened to chose steal if she did not agree to share her winnings with him to some extent.”
In a recent episode of the same game show, a contestant followed a similar strategy to that I suggested Steve should have taken. Watch the clip below, from a February 2012 episode of Golden Balls.
In this episode, Nick immediately takes control of the negotiations by insisting that he is going to steal, which is a very unorthodox approach to this game, in which the traditional strategy is to try and convince your opponent that you are going to split. By establishing a credible threat to steal, Nick puts all the pressure on Ibraham to decide only one of two things:
- Does Ibraham trust that Nick will split the money with him after he has stolen the full jackpot, and
- Would Ibraham rather both of them go home without any money at all than Nick win the jackpot and possibly not split it with him later on?
- Choose steal and go home with nothing.
- Choose split and have a 50/50 chance of going home with half the jackpot (based on his level of confidence in Nick's promise to split the money after the show).
- If he splits: 0 pounds or 0.5(14,000) = 7,000 pounds
- If he steals: 0 pounds or 0 pounds (assuming his confidence level in Nick's intention to steal is 100%).
- If you split: 0 pounds or half the jackpot
- If you steal: 0 pounds or the whole jackpot.
Rarely does such a perfect illustration of the Prisoner's Dilemma come along for Econ teachers to use in their classroom:
The payoffs are clear:
Each player has a weakly dominant strategy, which is to choose to steal. By choosing to steal, the player has a chance at maximizing his own payoff, but will do no worse than he would if his opponent also chooses to steal and at least will have the satisfaction of thwarting his opponent's attempt to steal the money.
There are three Nash equilibria in the game, which are outcomes at which a player can not do better on his or her own by changing his or her strategy. The outcome Steve was hoping for by chosing “split” (50/50) was not a Nash equilibrium because Sarah knows she can do better if she chooses steal when Steve chooses split. Steve doomed himself by choosing split because he should know that Sarah's dominant strategy is to choose steal. However, Sarah would also have doomed herself by choosing split because she should assume that Steve would also chose steal since steal is a dominant strategy for him too.
John Nash, who pioneered the field of Game Theory, assumed that humans were coldly rational, self-interested, deceptive creatures that would not hesitate to stab one another in the back to get what was best for themselves. His theory of human behavior is only partially proven correct in this game, in which Steve is shown to be the sucker and Sarah the coldly rational self-interested player. The best chance for Steve to go home with any money would have been for him to use the one minute of discussion time to convince Sarah that he would choose SPLIT, yet be willing to go home with something LESS THAN $50,000 and accept that Sarah was going to choose STEAL. He could have threatened to chose steal if she did not agree to share her winnings with him to some extent. Then again, any promise Sarah makes she could later break, thus further empowering the players to choose steal.
- What in the world is going on here? Why did Sarah choose steal rather than collaborate with Steve and share the $100,000?
- Was Steve totally wrong to choose split? What would you have done in his situation?
- How do the choices faced by Steve and Sarah relate to the choices faced by firms in oligopolitic markets? Now that you've seen this video, can you explain why collusive agreements between oligopolists often fall apart? Why do cartels such as OPEC often fail to achieve the high price targets agreed upon in meetings of their leaders?