Apr 20 2012

UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior!

The excellent Radiolab has now done a story about Golden Balls. After watching the videos and reading the post below, listen to this story.


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:

  1. Does Ibraham trust that Nick will split the money with him after he has stolen the full jackpot, and
  2. 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:
Teaching the Prisoners’ Dilemma Will Never Be the Same Again « Cheap Talk

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:

  1. What in the world is going on here? Why did Sarah choose steal rather than collaborate with Steve and share the $100,000?
  2. Was Steve totally wrong to choose split? What would you have done in his situation?
  3. 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?

About the author:  Jason Welker teaches International Baccalaureate and Advanced Placement Economics at Zurich International School in Switzerland. In addition to publishing various online resources for economics students and teachers, Jason developed the online version of the Economics course for the IB and is has authored two Economics textbooks: Pearson Baccalaureate’s Economics for the IB Diploma and REA’s AP Macroeconomics Crash Course. Jason is a native of the Pacific Northwest of the United States, and is a passionate adventurer, who considers himself a skier / mountain biker who teaches Economics in his free time. He and his wife keep a ski chalet in the mountains of Northern Idaho, which now that they live in the Swiss Alps gets far too little use. Read more posts by this author

112 responses so far

112 Responses to “UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior!”

  1. Philippaon 05 Feb 2011 at 1:49 pm

    1. What in the world is going on here? Why did Sarah choose steal rather than collaborate with Steve and share the $100,000?

    Because Sarah had made Steve genuinely promise that he was going to “split”, the rationally economic thing for her, the self-interested human, to do was to “steal” because she knew that she could steal all the wealth.

    2. Was Steve totally wrong to choose split? What would you have done in his situation?

    Economically, Steve was wrong to choose to split because if he had considered his strategies pertaining to the pay-off matrix, he would have realized that he could either steal all the wealth, or steal the chance for his opponent to steal all the wealth from him. Either way, he would have gone away feeling satisfied. Depending on the circumstances, I would have chosen different options. If I didn’t like or believe the player, I would have stolen, but if I was Sarah in this game, I would have split because I believed that Steve was going to split.

    3. 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?

    Firms in Oligopolistic markets are interdependent and must consider the actions of their rival firms. An example would be the decision about whether to advertise a product or not. Advertising costs money, increasing the firm’s costs and potentially decreasing profits, therefore the firm could be better off not advertising. However, if the rival firm chose to advertise, the loss would be much greater to the other firm than if they both advertised. Therefore, the dominant strategy would be to advertise, regardless of what the rival firm does. Oligopolies involved in collusive agreements are also coldly selfish, economically wise firms, and will always try to maximize profits, regardless of the ‘back stabbing’ it involves. This is why cartels such as OPEC fail to meet high prices, because individual firms in the long run don’t abide by the rules that were set in the leader meetings.

  2. Juan_Manuel_Arguedason 06 Feb 2011 at 1:53 am

    Well, for the first question, what is going on is a person who wants to share the final price and a person who wants it all. Sarah choose steal rather than collaborate with Steve and share the $100,00 because she had two arguements. The first one is that she was so convinced that Steve would choose split because she believed what he said. The other arguement is that she wanted all the money, and by having the first arguement, then she would definitely win all the price.

    Steve was not totally wrong, now that he was confident that Sarah would choose split, due to the horrorized face he did when he read, steal. He wasn't wrong also because he wanted to share, and was not selfish. I would have chosen split as well because I would love to have $100,000 just to myself, but being selfish is another completely different and very bad thing to do.

    The choices faced by Steve and sarah relate to the choices faced by firms in the oligopolistic markets by showing that firms are interdependent from each other. If one firm has better qualities and better in everything, then obviously that firm will win everything. Collusive agreements between oligopolists often fall apart because firms just want the best for themselves. Cartels such as OPEC often fail to achieve the high price targets agreed upon in meetings of their leaders because fo the same reasons. Since others will just be selfish, then they won't achieve anything.

  3. Juan_Manuel_Arguedason 06 Feb 2011 at 2:08 am

    @Saugata

    I agree with you with your first answer. This is because I also believe that Sarah knew or trusted Steve that he would choose split instead of steal. This would make her confident about choosing steal.

  4. Suyeon Soon 25 Feb 2011 at 6:12 am

    1. I think Sarah choose to steal because she wanted to maximize her profit. According to the Nash equilibrium, she would get $10,0000 if she steals from Steve. And since she wasn’t able to fully trust Steve whether he would choose split or steal, it would be the best to choose steal because if both choose steal, then both wouldn’t get anything, which sounds kind of fair, but if Steve choose split, then Sarah would get all the money, which is the best option for her.

    2. I don’t think his choice was totally wrong. When we look at the percentage, since it is considered to be the safest way that can satisfy both people in this game show. I think it was the matter of trust. Steve trusted Sarah and thought that she would split the money so both of them would be satisfied from the result. However, Sarah suddenly betrayed based on her desire to earn more money. So it could be said that the miscalculation about the other’s intention was the reason why he lost this game, but his choice itself was not a bad choice.

    3. This could be applied to the oligopolitic market, because like the game show, only few people are in the market and willing to split the large amount of money to satisfy their desire. In oligopoly, there are only few big corporations in the market that want to share profits from that market. I think that’s why corporations sometimes collaborate to increase or decrease the price of goods together, so both of them would be able to earn money. In Korea, for instance, the school uniform market is a oligopoly since there are only three companies that make school uniforms for all the high schools in Korea, and the three companies were accused for increasing the cost of school uniform together, to magnify their profit. However, this negotiation would not work sometimes if one betrays the others. In the market, if there are similar products, people tend to buy cheaper one. So though they promised to increase the price of their goods, if one company keeps their price low, then their profit would increase but others would not, because consumers would only buy the cheaper goods.

  5. Suyeon Soon 25 Feb 2011 at 6:15 am

    @Juan Manuel Arguedas Rodriguez

    I think your answer for the first one is really good. You described how did Sarah's way of thinking developed to make final decision. And i totally agree with your second and the third answer.

  6. Gökçe G&on 18 Mar 2011 at 8:35 am

    *Sarah realized that since Steve was going to choose split, she could choose steal and take all the money rather than half of it. She was taking a risk that Steve wasn’t going to also choose steal, because she would leave with nothing, but the risk paid off well.

    *Steve was hoping that Sarah would also choose split, which isn’t that bad of an assumption. I would have done the same in his situation because choosing steal just seems so rude.

    *The choices are similar because you make your decisions based on what you think the other will do. Collusive agreements often fall through because one firm will undercut the others for their own gain. The collusive agreement is the same as the split ball.

  7. Muhammet_Emin_Uylason 18 Mar 2011 at 3:37 pm

    1.Because when Sarah choose steal, she may maximize her profit rather than sharing profit but she is taking risk because Steve may also choose steal so both may lose money. By choosing steal Sarah may profit 100k if Steve wants to have profit so this strategy is better for Sarah.

    2.Steve wasn’t totally wrong while he is choosing split because it is more humanistic choose in that deal because if Sarah also choose split they will share profit equally but there is risk on choosing split because Sarah may not want to share profit and she can choose steal to maximize her profit.

    3.In oligopolistic markets, firms should also have strategies while they are deciding on prices because it may affect them badly or they can maximize their profits so it is same as oligopolistic markets. And we can see hear collusive agreements between oligopolists often fall apart because they cannot maximize their profits. Lastly, cartel may also fail markets because again they cannot reach maximum price to maximize their profits and by doing that firms are sharing their profits.

  8. Nesibe Zirzak?ranon 18 Mar 2011 at 4:09 pm

    1. What in the world is going on here? Why did Sarah choose steal rather than collaborate with Steve and share the $100,000?

    Sarah chooses steal rather than collaborating with Steve because she wants to maximize her profit, if she shared it with Steve, they would have to equallly share the money gained.

    2. 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?ü

    It is like the model of oligopolistic markets. They consider their maximum profit and behave according to it. Firms should come up with strategies in order to gain maximum profit and in this situation Sarah chose to steal because it was the most maximizing process.

  9. Arthuron 29 Apr 2012 at 9:15 pm

    Hi there, I've written about the Nick/Ibrahim game here if anyone is interested: http://www.tutor2u.net/blog/index.php/economics/c… Feedback is highly welcome. :)

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    UPDATE: Golden Balls, Game Theory, the Prisoner’s Dilemma, and the cold rationality of human behavior! | Economics in Plain English

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