The point is that a promise to split is not convincing, but a promise to steal is. Interesting.

This view is wrong because what matters to Ibrahim is that Nick cannot credibly commit himself to splitting the money after the show just by announcing his intention to do so. The game Nick and Ibrahim are playing cannot be turned into a chicken game in the way Nick proceeded because Nick had no way to force himself to split the money after the show.

How could Ibrahim know that Nick will really split the money with him? Nick’s strategy could simply be a clever but risky way of persuading Ibrahim to play “Split” so that he, Nick, can walk away with the whole jackpot himself.

Nick made an attempt to force Ibrahim to trust him. In response, as Phil argued, Ibrahim could have reasoned: I don’t like being forced into trusting Nick; I’m proposing that I’m playing “Steal”, and you Nick play “Split”, and I’ll split the money with you after the show. Remember that once you have persuaded your opponent to trust you, you face the temptation to double-cross him. That’s the devilish logic of the prisoners’ dilemma. One of the key definitional characteristics of this dilemma is that the players cannot make credible commitments – that is why allowing pre-play communication between the players does not change the logic of the prisoners’ dilemma. (In real life, the possibility of pre-play communication between the players does change the way people play the game, but the strategy/outcome matrix does not change. The players can still attempt to double-cross each other: Just go to youtube and watch a few clips from this show.)

After Nick has announced his ultimatum Ibrahim’s choices are as follows:
1. He can accept that Nick will play “Steal”, in which case Ibrahim’s chooses between:
- “Not being the sucker (only loser)” for sure, by playing “Steal” and,
- a lottery with 2 outcomes (given that Ibrahim cannot know whether Nick will keep his promise to split the money after the show): winning half the money or being the sucker/only loser, by playing “Split”

2. Ibrahim could also counter Nick’s ultimatum with the proposal that he, Ibrahim, will play “Steal” and Nick play “Split”, and he promises to split the money with Nick after the show … and then Nick and Ibrahim try to bully each other into playing “Split” while promising to split the money after the show (without being able to commit themselves to keep the promise).

So after Nick has announced his ultimatum, Ibrahim is in the SAME position as before. He can play either “Split” or “Steal”, and he can end up as the only winner, the sucker/only loser, with half the money, or with no money while Nick doesn’t win any money either. Ergo: Nick’s ultimatum changed nothing.

Nick played the game with ingenuity but his strategy did not change the type of game they were playing. It could have ended differently for him if he had played against another opponent.

1) Despite the fairly obvious conclusion that stealing cannot make you leave the show with less that splitting would, splitting is quite common. In 31% both split, 44% one split and 25% both stole. People are either not able to work out that splitting cannot make you better off, or they are valuing something else quite highly. AS Ken B says, contestents are not playing a one-shot game. The clip shown above shows that Nick values “winning” the game above taking home more money. For him, winning meant a succesful cooperation. For others, winning might mean succesfully suckering the other one.

2) The “small peanuts” effect. When playing for “small” stakes of a few hundred dollars, people were much more likely to cooperate. This is interpreted that they would rather be seen as cooperating than win such a small sum. However, the sum would be considerd large in most contexts, and huge compared to sums used in university research. This “context” effect disppeared at £1500, above which cooperation rates were unrelated to prize money.

3) There was significant “reciprocal” tendency not to cooperate with those who had tried to get one voted off in earlier rounds.

4) There was no evidence of expectational conditional cooperation. Either people could not predict cooperation, or they had no reciprocal tendencies. Given the strong reciprocal tendency above, it seems that people could not predict who was going to cooperate. However, saying that you were going to split was the strongest predictor of whether you actually did – those who made an explicit promise to split were 33% more likely to do so. Since people could not predict who would split, it seems we are missing out on an obvious source of information – that people often do what they say.

1. If you think Nick did well aggressively putting Ib on the spot, then it’s not the strategy that is great. Strategies are understood out of context, not in the context that you have a bully and a duck.

2. It’s not irrational for Ib to try to turn the tables if it wasn’t irrational for Nick to do what he did in the first place. If Ib turned out to be a bigger bully and can say I heard what you said, I’m stealing it would make Nick’s choice to steal irrational. We don’t attribute Nick with irrationality and so you cant say Ib would be. There’s nothing special about being first to the poll unless Nick actually shows Ib that he has thrown away split, Ib can mirror the tactic

It still is clearly prisoners dilemma until Ib ultimately proves himself to be a duck who has been outplayed. But that is the context of this particular match, not anything to do with the general strategy employed. It’s a dilemma for a reason.

Given what Nick had already established halfway through the negotiations, that would have been irrational behaviour on Ib’s part.

He didn’t change the game at all. What’s to prevent Ib from saying, no, Nick, you listen to me. ” I AM GOING TO STEAL. YOU back down, you pick split, and guess what I might give you 1/8, because the expected value of Prize/8*I’m not screwing you is still better than 0.”

If I’m Ibrahim I say, hey Nick we can talk all day. But here’s my split ball, see, and I throw it across the room. There’s no reason Ibrahim cannot turn the table on Nick, and so Nick’s genius was his his read of Ibrahim, not his strategy.

Nick doesn’t better his chances. He still has to rely on Ibrahim to go along otherwise he could end up with 0.

“Golden Balls has attracted attention from social scientists as a natural experiment on cooperation. A team of economists including Richard Thaler have analyzed the decisions of the final contestants and found, among others, the following …” (http://ssrn.com/abstract=1592456)

Would there be an enforcement problem (or would enforcement require the action of a third party)? No.
An enforcement problem would only arise if you could not trust your own eyes (that is, if there were a way to be deceived about whether the other player is opening the ball I handed him/her). When I give you my “Split” ball to open, I’ll only stick to our agreement to open the ball you gave me, if I’m 100% certain – that is, when I observe – that you are actually opening the ball I gave you. So I can make my cooperation conditional on observing your cooperation. If I think that somehow you managed to exchange the ball I gave you (a “Split” ball) against the one you kept (a “Steal” ball), I can just demand that we engage in another round of picking strategy for each other.

If the other player does not accept this proposed strategy I’d just play “Steal”.

I also agree that Nick’s strategy is quite ingenious. However, it does require that either a) Ibrahim trusts Nick to some degree or b) doesn’t consider the outcome “Nick steals, I split, and Nick doesn’t split the money” as the absolutely worst outcome. Regarding b), Ibrahim could reason: Yeah, I’d like to split with Nick, but I have no clue whether he’ll keep his promise to split the money with me after the show AND I would really hate to end up as the sucker!

In other words to play “Steal” you don’t have to be stupid or greedy. It’s enough to doubt sufficiently strongly that your opponent will play “Split” AND to desire not to be the sucker in the game.

Ergo: Nick played in a clever way but he could have lost if either a) Ibrahim had not trusted him to some extent or b) with Ibrahim not trusting Nick at all, Ibrahim had preferred not to be the sucker, i.e., prefering taking the risk that both lose over the risk that only he himself loses (= being the sucker in the game).

As far as I can see, the strategy proposed by AlexS doesn’t require any trust because whether a player sticks to the agreement or not is observable.