UK Game Show Golden Balls: A New Solution to the Prisoner’s Dilemma

Several years ago, Felix Oberholzer-Gee, Joel Waldfogel and Matthew W. White, published a fascinating empirical article about the prisoner’s dilemma game embedded in the short-lived U.S. game show “Friend or Foe.”  Their core findings:

Using data from two seasons of a television game show, we provide evidence about how individuals implement conditionally cooperative preferences. We show that (1) contestants forgo large sums of money to be cooperative, (2) players cooperate at heightened levels when their opponents are predictably cooperative, and (3) players whose observable characteristics predict less cooperation fare worse (monetarily) over time, as opponents avoid cooperating with them. 

I always thought it might be nice to update the study to test to see whether different kinds of “cheap talk” were more or less effective in establishing cooperation (ex. Does swearing an oath to God make your promise more credible?). 

It might be time for a follow up: The UK game show “Golden Balls” (sounds like an Austin Power’s character) ends with the same PD conflict – as two contestants have to decide after a 30-second discussion whether to “split” or “steal” the big prize. This clip shows a contestant who devised an amazing (but possibly not repeatable) solution to the dilemma:


Caleb b

What percentage of contestants look inside both balls "just to see," even though you only need to check one ball? I bet it's either 100% or close to it.

Systemsguy

It's interesting to figure out why the right-hand guy's strategy works in this encounter.

Each player initially has 3 outcomes to think about. A player can get all, half, or none of the money. But when the right-hand guy insists in advance that he is going to Steal, he reduces his opponent's possible outcomes to half or none. Since a chance at half is better than a certainty of none, the left-hand guy naturally chooses Split, so they both win. A seemingly irrational gambit forces a rational opponent to do what is best for both of them, so it turns out not to be irrational after all!

Incidentally, this is not a true Prisoner's Dilemma game, because if your opponent chooses Steal, you get the same thing (nothing) whether you choose Split or Steal. In true PD, it is always better to defect (choose Steal) if you know that your opponent is going to defect (choose Steal).

Also, the sum of the rewards in this game is the same as long as at least one player chooses Split: 2xHalf = None+All. To make this more like a real PD, the payoffs might be something like 10, 7, 0, creating a positive sum for cooperation: 2x7 > 0+10. But that would mean that the strategy illustrated in the video would seem even MORE irrational - and might be more likely to backfire - because the offer to split the reward afterward would have a lower payoff per person (5) than true cooperation (7).

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metalate

It's pretty similar to a true Prisoner’s Dilemma. PD still works if the prisoners are allowed to discuss their strategy BEFORE the decision-making time, as is allowed here. Crooks could decide before the heist to refuse to talk in the event they are caught, just as players here can talk before they pick balls. But once you have to choose, it's still better to make the opposite choice.

Arthur

Hi there, I've written about the game here if anyone is interested: http://www.tutor2u.net/blog/index.php/economics/comments/game-show-game-theory Feedback is highly welcome. :)

Cameron

My tactic would be to pick a ball and then say 'here, I'll trade with you', and trade balls.
Don't know if that would be formally allowed :)

Travis Idol

I disagree that Ibrahim held out a sliver of hope that Nick was lying. I think the ingenious part of Nick's strategy was that he changed the dilemma for Ibrahim from a monetary one to a purely moral one, and the rules of Golden Balls actually made it possible. It's the classic hero-villain drama in which the villain is self-consciously evil and the hero is thus defined as his moral opposite. The rules of GB, by not being a true PD, meant Ibrahim was going to get nothing if Nick was honest about his intention, so there was no monetary dilemma for Ibrahim anymore. Instead, Ibrahim had to choose whether he was going to respond as a hero (choose split) or act out of frustration and spite (choose steal). Yes, the audience would have probably cheered for Ibrahim had he chosen steal and won everything, but Nick would have "won" the moral contest by showing Ibrahim that he was no hero. I think the telling comment from Ibrahim was that his Dad told him that a real man keeps his word. In that comment, he declared himself to be the hero. What would really be interesting is if Nick picked up on that comment and decided then and there to choose split rather than steal. In any case, I wouldn't want to play poker with Nick.

[WORDPRESS HASHCASH] The poster sent us '0 which is not a hashcash value.

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Glennn

It's worth noting that a recent RadioLab podcast (http://www.radiolab.org/story/golden-rule/) discussed this case, and interviewed both men. Ibrahim admitted his comments about his Dad were a lie and he had been intending to steel until this strategy on Nick's part. Indeed, Ibrahim admitted that he never knew his father as a child, and had taken this line from a movie he'd watched.

matan

hi Ian,

can you please better explain me the quote of: "Using data from two seasons of a television game show, we provide evidence about how individuals implement conditionally cooperative preferences. We show that (1) contestants forgo large sums of money to be cooperative, (2) players cooperate at heightened levels when their opponents are predictably cooperative, and (3) players whose observable characteristics predict less cooperation fare worse (monetarily) over time, as opponents avoid cooperating with them. "

thank you
Matan
Website

Robin

I have been trying to find out exactly how many cash balls were ever used in Golden Balls? Does anyone know?

Manpreet Singh

Given the rather modest amount of prize money, I think that the primary incentive to 'steal' in this game is to avoid the embarrassment of having been fooled in front of a national audience. In this particular instance, Nick removed that incentive for Ibrahim to 'steal' by simply announcing that he plans to steal, thus ruling out the possibility of Ibrahim being fooled. Also, given that Nick will definitely 'steal', Ibrahim must be indifferent between his two choices of 'steal' and 'split', because he is sure to win nothing, irrespective of his choice.

With both the conventional reasons to choose one way or another thrown out the window, I'm trying to think what exactly nudged him to 'split'. Was it:
* excitement about the remote possibility that Nick has been playing all along and actually plans to 'split'?
* an expectation that the society will hate Nick and respect Ibrahim, if Ibrahim 'splits' while Nick 'steals', because of Nick's maturity and wisdom in letting someone win, even if he couldn't?
* the remote possibility that Nick might be sincere about his promise of sharing the reward after the game if Ibrahim 'splits', and the absolute certainty of zero gain if Ibrahim 'steals'

Wow, this is an interesting situation!

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