Golden Balls Prisoner's Dilemma
Wednesday, April 25, 2012 at 9:26PM 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)
With all due respect Dude, your view on this is idealistic bordering naive. Nick has no obligation to share the money in the event of Ibrahim split, Nick steal, despite verbally agreeing to it. As Jasper (the presenter) stated, there is no legal obligation. The only legal and guaranteed way Ibrahim can get half of the money is in the case of split split.
Basic Scenario:
Abe can take a guarenteed 0 or a chance of splitting after the show. Some chance is better then no chance. Clearly if he believes Nick will steal then he must choose split. By removing Abe's belief that Nick will chooose to split ever, Nick has made Abe's better choice to select split given the circumstances.
However, this leads to the question, if Nick knew Abe would split why not just choose steal and double his prize. Well, even with his solid yomi, I think there was a little more to the scenario that was being under valued.
Extra Scenario:
And this leads me to the second scenario. The second scenario that was created by his promising to split after the show. This promising to split and then later selecting split showed Nick that Abe was a good guy and had all intensions of keeping his word and that he only said what he said to elict a certain response from Nick. Also, it implanted the idea in Nicks head of after the show splitting. Prior to that it had been only what happens on the game show counts and nothing happens after. After the show splitting can only occur if one of the player holds the money. So Abe had to choose split to ensure that the money would still be in play after the game. Regardless of what scared Nick chose, Abes choice of split would keep the money in play even if Nick was spiteful. Nick's speech of honor also helped add to the chance that if he chose to be spiteful in the heat of the moment that he may be able to choose a fairer option after seeing the honor in Abe's move. So Abe's move was to guarentee that the money would stay in play instead of risking all the money on a guy not being spiteful.
Compared to standard prisoner dilemma :
There is a problem with this verse standard prisoners dilemma. The problem with this and the reason that they won is that steal is not always the single best option. If the opponent chooses to steal then no matter what I do I end up with nothing. So while steal is the best option if my opponent steals, it is only equal to split. Since steal and split are equal if my opponent chooses to steal (for me), I have no reason to choose one over the other in that scenario. But in standard prisoners dilemma if my opponent chose to call me guilty and I called him innocent he would get 0 years in jail while I got 10. But if we both said guilty then we would both only get 5. And if we both said innocent then we would both get 2. In this case saying he is innocent always results in a worse outcome for me (as opposed to saying guilty). If he says guilty and I say guilty I only get 5 years as opposed to the 10 I would get had I said he was innocent. Also, if he said innocent and I said guilty I would get 0 years as opposed to the 2 I would get had I said innocent.
If the game was changed to mirror this idea then the decision could have become more difficult. Lets change the rules so if both choose split they don't split but instead both get the prize money amount (splitting double the prize money). Now is one chooses steal and the other split then the stealer gets double the prize money and the other guy gets 0. Now lets suppose if they both pick steal then that causes them to split the prize money (only getting half the prize money each). This would have made the choice far more difficult for Abe. He could take half the prize money or wager on Nick. In that scenario half the prize money is better then 0 and it be hard to turn down. There would be a numerical advantage to stealing in this game. Verses the actual game where if my opponent steals both of my options lead me to end up with 0.
Just my two cents...
Just imagine that Nick only has 1 ball in front of him: the Steal ball.
Then the options for Abraham are:
1) Steal = guaranteed $0.
2) Split = chance to get $6000+.
It's not a common strategy because it's not Prisoner's dilemma.
The traditional prisoner's dilemma will offer a 5/5 for a split, a 9/0 for a 1 sided steal, and a 1/1 for a double steal. The TV version here gives Abraham (conveniently, player A) no incentive to steal if Brian's declared strategy (conveniently, player B) is always stealing.
The TV version may be exploitable, but it's certainly easier to explain to an audience, and honestly, the exploitation made for good television.