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Wednesday
Apr252012

Golden Balls Prisoner's Dilemma

You might have seen this video going around:

Watch it first, then I will say some things...

 

Ok, read on if you watched it.

I've seen some kind of overly complicated explanations of Nick's strategy, so I will give you my explanation. Nick wants to split the prize 50/50 which is understandable because that's the overall most fair outcome for both players. If his goal is to split 50/50, the one thing that will mess that up is if Abraham chooses to steal. So what Nick should do is say whatever needs to be said that would convince Abraham not to steal. This lie is actually to benefit *both* of them and ensure a fair outcome.

Nick's claim that Nick will steal leaves Abraham with the choices of a) steal (where Abraham gets nothing) or b) split (where Abraham might get 50% of the prize if Nick follows through with his promise). Abraham might choose to get nothing out of spite, but if Nick can appear genuine then he bets that a chance at 50/50 split will be more attractive that "guaranteed" getting nothing. Nick's strategy (which requires Nick to appear very confident and genuine) does deter Abraham from stealing.

If Abraham is deterred from stealing, then Nick can go ahead with splitting. Yeah Nick said he would steal, but if Nick's intention all along is to ensure a 50/50 split, there is actually no reason for him to go through with his claimed plan of stealing, then sending Abraham half the money later. Instead, now that he has "defused the bomb of the possible steal," he can simply choose split. Again, the lie was actually to benefit both players.

The only thing I'm not sure about here is why this has not been a common strategy for years. Maybe it has, though the recent popularity of this video would lead me to believe it was an unusual move.

Reader Comments (24)

The problem with that show is that it never makes sense to pick anything other than the Steal ball, if the other guy picks steal you get nothing either way, if he picks split you can either have half the money (split) or all of it (pick steal) so the only real logical option is to convince the other guy to split and go steal yourself.

April 25, 2012 | Unregistered CommenterEamonn

I would suppose this strategy relies entirely on Abraham thinking that Nick sincerely will always go 'Steal' and so he is better off going 'Split' himself for a the off-chance of some return.

If Abraham could see through this deception, and had chosen 'Steal' rationally, or out of spite, he would have achieved a better result.

So as soon as this strategy becomes popular, the party faced with the threat will be more inclined to 'Steal', effectively making this strategy self-defeating over multiple games. (Assuming that only one party seeks to achieve a 50/50 scenario).

Forgive me if my analysis is naive.

April 25, 2012 | Unregistered CommenterNick

If it were a well-known strategy or Abraham was expecting it for some other reason, then Abraham could act exactly as he does in the video but actually steal. I think nick should have publicly acknowledged this possibility and gone ahead to actually steal. of course, Abraham might realize he can make the same ultimatum. If that happened it would turn into a game of chicken I guess.

April 25, 2012 | Unregistered Commentermatt

As you correctly identified this ONLY works if Abraham believes that Nick will steal regardless, but I think you're neglecting that it also only works if Abraham TRUSTS nick and WANTS to split. Had Abraham not believed Nicks good intentions he could looks at the situation as "I get no money either way" and gone for steal just to ensure his opponent got none.

Replace Abraham with a more greedy player(which if you've ever seen other episodes there are PLENTY) who is aware it might be a ploy and choosing steal might seem like the most beneficial outcome. Heck I wouldn't put it past some of these players to use Nick's strategy, except they'd actually steal in the end and not split the cash.

April 26, 2012 | Unregistered CommenterEji

I don't see how this could go on to be a common strategy because isn't the strength of the tactic in the novelty? Abraham's surprise at the choice he was being forced to make is what caused him to accept choosing split out of desperation. But if people commonly made the "Nick Claim" and it wasn't surprising, an Abraham would have no special reason to trust that they weren't just double-bluffing it instead. And you're essentially back to square one.

April 26, 2012 | Unregistered CommenterLizard Dude

Lizard Dude, yes right. I meant it seems weird that it would be novel at this late date, but apparently it is. You'd think it would have started to be common, then not work because it's known (as you said), and no longer be newsworthy. Yet I saw it linked many times lately.

April 26, 2012 | Registered CommenterSirlin

"If Abraham could see through this deception, and had chosen 'Steal' rationally, or out of spite, he would have achieved a better result."

It's possible that Nick was factoring in the possibility that Abraham would have felt bad about that result and shared the money afterward, after realizing what Nick was trying to do. Maybe NIck had a decent read on Abraham as well, such that Nick had a pretty good idea how Abraham would act.

April 26, 2012 | Unregistered CommenterThreeup

This strategy reminds me somewhat of stuff covered in Thomas Schelling's 'Strategy of Conflict' (which is basically The Prince if it were written after the development of game theory). Are you familiar with the text, Sirlin?

April 26, 2012 | Unregistered Commenterhamiltonianurst

"I don't see how this could go on to be a common strategy because isn't the strength of the tactic in the novelty?"

Not necessarily. The typical behavior of people is to split windfalls into equal parts even if the contributions are unequal. In the video, the moderator is pushing pretty hard to create tension and convince them that they can 'get away' with 'stealing' - like Glaucon with his ring of invisibility: "There's no legal requirement..."

In fact, as long as you're willing to split, the reverse gambit of getting the other guy to agree to steal the money might be a stronger play.

The best part of the video, of course, is actually when one of the Abraham reveals he has a yacht at the end.

April 26, 2012 | Unregistered CommenterNate

Hi Sirlin,

By "overly complicated explanations of Nick's strategy" are you referring about game theory? I was wondering what types of math tools do you use to design and balance your games (game theory, probability theory...)?

April 26, 2012 | Unregistered CommenterLuc Trudeau

Eamonn: You're making an error common in Economics and business theory by assuming that profit maximization is the preferred and natural behavior of human beings. It isn't, which is why the Prisoner's Dilemma rarely works out the way it's supposed to in the real world.

People genuinely value fair-dealing; this is why people prefer set-price systems to barter ones, and why most consumers are willing to pay a higher price for brands of proven quality rather than always choose the lower price or black-market equivalent and risk getting ripped off. Humans are also naturally social animals, meaning that considerations of reputation and equity are just as important and "logical" as ones of bare profit in our decision making. As such, there's nothing "irrational" about choosing split in this game; when someone does so it simply means they value reputation, maintaining relationships, and general equity over being "the winner" in a contest. To put it simply, only a very small number of humans are sociopaths, and it's illogical for us to expect all humans to behave as that slim minority does.

April 26, 2012 | Unregistered CommenterHeron

This reminds me of a pretty fun Japanese drama called "Liar's Game". Check it out. The whole thing is about people competing in different games with this theme of trust and greed. The premise there is that this shadow organization gives each player a loan of $1,000,000. At the end of the game they have to return the loan to the organization or else be in debt. So if everyone agrees to "split" then no one will go into debt, but no one will get rich either.

Back to this actual show, two potential strategies:
1) bring a contract with you and get the other person to sign it, agreeing to split the money in some way.
2) expose your ball contents to eachother

Back to Liars Game:
Sirlin, I know you're too busy, but I'd love to see your analysis of the various games that they play in that drama. Like, is there really a full prove win strategy or do the winners win just because of the drama's writers?

April 26, 2012 | Unregistered CommenterThomas Grové

I have to chuckle at the people who say "of course you should steal." Yes, I understand Nash Equilibria. The whole point of the Prisoner's Dilemma is that the Nash Equilibrium sucks. The brilliance of the guy's strategy is convincing the opponent that the payoffs have shifted such that the weakly dominant strategy is no longer dominant. That's awesome.

I saw the REAL equilibrium strategy for this game on another forum: Open the discussion period by saying "If you look at the notes, I will steal. But I won't look if you won't." This gives both players an EV of 3/8 of the prize money (not that much less than half) without needing to trust the other player.

April 26, 2012 | Unregistered CommenterChad Miller

WONDERFUL! ABSOLUTELY WONDERFUL!!!
I myself randomly stumbed upon videos of this game show on youtube like half a month ago. And after watching a dozen of them or so I myself thought of this EXACT STRATEGY!! I'm just so happy right now this dude actually managed to get on that show and DO THIS!!! EXCELLENT :DD
This guy is great!
And I'm so happy :))

April 26, 2012 | Unregistered Commenterfriiik

There is another side to his strategy, which requires him to choose split in the end. Assume that his strategy is to eliminate risk.

He claims that he will steal, and split it after the show. He chooses split.

If the other guy splits, they both get what they wanted.

If the other guy steals out of spite, then by the previous conversation, the other guy is STRONGLY pressured into splitting anyway after the show.

In either case, he wins.

April 26, 2012 | Unregistered CommenterFieari

> The problem with that show is that it never makes sense to pick anything other than the
> Steal ball, if the other guy picks steal you get nothing either way, if he picks split you can
> either have half the money (split) or all of it (pick steal) so the only real logical option is to
> convince the other guy to split and go steal yourself.

No, I don't think so. Even though this isn't technically a generalized form of PD (AIUI both defect has to have a worse payoff than I coop and you defect) ... it should be pretty obvious that if both players always defect it's much worse for them than if they both coop.

Of course the main problem is that you only get one shot at it, whereas computer PD tournaments tend to be "iterated".

April 29, 2012 | Unregistered CommenterJames Antill

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

April 30, 2012 | Unregistered CommenterArthur

The classic Prisoner's Dilemma problem doesn't allow for communication between both of the parties. In this clip, Nick is taking advantage of that and changing the rules of the game. Nick changed it to a game of Chicken, and he's put a brick on the gas pedal, a blindfold over his eyes and removed the steering wheel so that his opponent has no real choice in the matter. This is different from Prisoner's Dilemma, where both parties have to make a choice and have no way of really figuring out what the other player will do.

May 3, 2012 | Unregistered CommenterMorzas

Morzas yeah I think that's an excellent point. I mean technically Nick doesn't have any limitations like you're saying, but he gives a very strong APPEARANCE of having them, which is almost as good.

The book The Strategy of Conflict explains in great detail the concept you just mentioned, that having limitations or obligations is very powerful in negotiation. Like if we are "negotiating" which of us will merge into the desired lane while driving, then it's a powerful negotiation tactic for me to be unable to see you. Or for me to be insane or unreasonable, and somehow make it clear I will get into the desired lane "no matter what, even if we both die" or something. This leaves you (or Abraham, as the case may be) with a different payoff matrix than if I don't do that.

May 3, 2012 | Registered CommenterSirlin

Where I live, a verbal agreement is every way as binding as a written and signed one. Only harder to prove.

And since he promises in front of a myriad witnessess, Abraham is golden.

May 4, 2012 | Unregistered CommenterDude
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