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?
Nick’s strategy is brilliant. By the end of the negotiation, Nick has convinced Ibraham 100% that he is going to steal the money. Ibraham may only have had a confidence level of 50% that Nick was honest about splitting the money with him after the show, but with a 50% confidence level, Ibrahim’s possible payoffs are:
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).
In other words, with a jackpot of 14,000 pounds, the payoffs for Ibrahim became:
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%).
Clearly Ibraham now has a dominant strategy: to split. In the typical version of this game, a player’s dominant strategy is always to steal (as explained below), since the possible payoffs are:
If you split: 0 pounds or half the jackpot
If you steal: 0 pounds or the whole jackpot.
But because Nick has convinced his opponent that he will steal, and then split the winnings, Ibraham’s dominant strategy shifted to split, since the possible payoffs have changed. Ultimately, Ibraham does what is most rational given his confidence in Nick’s threat to steal, and that is to split. Ibraham then chooses split (as he should), but then to everyone’s surprise, Nick chooses split, not steal as he had threatened to do throughout the negotiation. This a surprising twist, since from Nick’s perspective stealing is clearly now a dominant strategy! Nick had convinved Ibraham to split, which means Nick faced a greater payoff by stealing. But by splitting, Nick shows that he had intended to split all along, but first needed to convince Ibraham otherwise to establish splitting as Ibraham’s dominant strategy.
What a thrilling game! I won’t even bother getting into how this relates to economics today, I’m still shaking with excitement over the outcome!
Original Golden Balls post:
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.
Discussion questions:
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?
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