April 22, 2012

"Possibly the best filmed example of game theory in action ever."

Metafilter points to this showdown on "Golden Balls":


Lyle said...

Guy on the right played well.

bagoh20 said...

There really is no strategy. You either trust the other guy or you don't. No matter what strategy you think is being used, it still comes down to that.

But, I think the strategy here was if the bald guy did take all the money, then he would feel obligated to give the other guy the same deal he was offered. Thus two bites at the apple.

Rabel said...

Speaking od Brits and balls, this review section from Amazon.uk has been going around the nets.

Pardon if it has already been linked.


Wince said...

While ostensibly demonstrating how both players can "win" the prisoner's dilemma, it didn't.

Apart from the lack of ability to coordinate in the true prisoner dilemma situation, there's no way to split the benefits after one prisoner testifies against the other.

Instead, Nic demonstrated the potential benefit in game theory of being the "the first throw the steering wheel out the car window" in order to gain control of the road.

The interesting insight from Game Theory is that a player that can credibly demonstrate that he lacks control and hence cannot swerve will win the game. For example, one driver might ostentatiously throw his steering wheel out the window. Onlookers may think that he is insane, but the demonstration forces the other driver to rethink his strategic choices. The sane player can dismiss the possibility that the crazy player will choose the chicken strategy. Having seen the crazy player’s steering wheel fly out the window, the sane player knows that he can no longer win the game or even play to a draw. He must concede. The sane player must be the chicken. Of course, the same logic holds of one player can credibly demonstrate that he delusional enough to believe that nothing bad can happen even if there is a collision. In a game of chicken, the crazy player has the advantage.

Nic didn't completely eliminate his ability to choose "split", obviously, nor could he. But by stating his unequivocal intention to chose the self-interested "steal", he removed any pretense of good-faith coordination within the game itself. That left Abraham with only two choices: (1) loose or (2) trust. Nic had diminished the potential benefit of Abraham's third option: deception. Nic's altruistic deception benefited both by curtailing Abraham's expected benefit of self-interested deception.

Aside, while the host alluded to there being no way to enforce Nic's promise to split the prize afterward (perhaps because the game show's rule prohibit it?), otherwise I can't think of a Statute of Frauds or other legal defense from making the oral agreement enforceable.

rhhardin said...

It's a coordination problem.

If R says he'll steal and then share, the only shot L has is to split.

If R steals, L gets half _probably_.

If R splits, L gets half.

If L steals, he's been promised that he'll get nothing.

So L's only option is split.

StoughtonSconnie said...

Classic Prisoner's Dilemma, except for money instead of avoiding prison time, which is why it works. I think the strategy here was to freeze out your opponent's choices. That's why Nick moved so quickly to announce to Ibrahim his intent. The optimal solution is that both players act in their self-interest, but since you can't do that outside of your opponent's choices, that means split. But to announce "I'm going to choose split" is to invite a loss. So you do what Nick did, hoping that your opponent will select split, and you do too. It puts you in control of your opponent.
The interesting thing is how sincere a liar Nick is. He has a future in politics!

Harsh Pencil said...

Every time a man is on first base and the pitcher and catcher must decide whether to pitch out is a filmed example of game theory in action.

And the theory does great. It predicts randomization on both sides.

Chip S. said...

It's not a Prisoner's Dilemma. Neither is "Chicken", btw.

In a PD, "share" is strictly dominated by "steal". In this game, "share" is only weakly dominated; if your opponent chooses "steal" your payoff is zero no matter what you do.

That's why even an uncertain chance of a post-game side payment can influence the outcome.

Cleverly done.

Zach said...

For a single round game between strangers, stealing is a degenerate strategy -- it's no worse than even regardless of the opponent. The only way you can change your expected payoff is to change your opponent's strategy -- here, by credibly committing to stealing, and offering a side deal.

Of course, once you've made that commitment, it's a zero cost strategy to break your promise and choose split instead. That way, you ensure that the disaster scenario is averted, and your opponent might even choose to split out of generosity in your new worst case scenario (split/steal, with all money going to your opponent).

Wince said...

Chip S
Neither is "Chicken", btw.

Funny, tasted like Chicken.

Admittedly, wasn't pure "Chicken", more like a Chicken Nugget. One reason I dubbed it "'the first [to] throw the steering wheel out the car window' in order to gain control of the road".

But how do you explain Nic's strategy of throwing away the option to coordinate within the game as having nothing to do with him using a "Chicken" strategy in way to overcome the Prisoner's Dilemma, as both are loosely applied to the predicament of this game show?

David said...

You mean we have to watch one thing for six minutes?
Holy attention span, Althouse, will this be on the exam?

William said...

Rational self interest doesn't motivate a lot of human behavior. See World War I.

Chip S. said...

EDH--As Nic played it, there is no apparent difference b/w his strategy and the strategy of announcing that he's going to choose "share" (b/c he chooses the 50/50 split). However, his strategy opens up more possible outcomes, b/c IF he's credible then he's turned the game into a single-round noncooperative bargaining game, in which he offers his opponent some token amount and keeps the rest.

What this game best illustrates, IMO, is the importance of the actual full rationality of the players. Among purely rational players, Nic's strategy is as good as his opponent's degree of belief that he'll carry it out. (And since he's only vulnerable if he deviates from it, his announcement has a high degree of credibility. The fact that he didn't follow through is part of this clip's viewer appeal.)

But in reality it is wise to consider your opponent's emotions. If Nic's opponent didn't believe that he'd share afterwards, then his payoff-indifference between "share" and "steal" could easily have been trumped by feelings of anger and resentment. So if Nic had enraged his opponent enough, this strategy wouldn't have worked.

Chip S. said...

EDH--Upon further thought I can see the merit in your "steering wheel" analogy, due to the high degree of credibiity of Nic's announcement in this case. My objection was based on the fact that Nic wasn't allowed to show what action he chose--and showing the removed steering wheel is critical to the whole "chicken solution".

And, after all, he didn't really throw away his steering wheel at all....

Wince said...

As Nic played it, there is no apparent difference b/w his strategy and the strategy of announcing that he's going to choose "share" (b/c he chooses the 50/50 split).

The difference I see is seeking an agreement within the game to "share" would increase the expected return to Abraham of following the share-deception strategy.

However, his strategy opens up more possible outcomes, b/c IF he's credible then he's turned the game into a single-round noncooperative bargaining game, in which he offers his opponent some token amount and keeps the rest.

Hmmm. Doesn't it reduce the possible outcomes (see bold text below)?

Friend or Foe?

Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the United States. It is an example of the prisoner's dilemma game tested by real people, but in an artificial setting. On the game show, three pairs of people compete. As each pair is eliminated, it plays a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the payoff matrix is slightly different from the standard one given above, as the payouts for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If you know your opponent is going to vote Foe, then your choice does not affect your winnings. In a certain sense, Friend or Foe has a payoff model between prisoner's dilemma and the game of Chicken.

This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls. The latter show has been analyzed by a team of economists. See: Split or Steal? Cooperative Behavior When the Stakes are Large.

Split or Steal? Cooperative Behavior When the Stakes are Large

We examine cooperative behavior when large sums of money are at stake, using data from the TV game show “Golden Balls.” At the end of each episode, contestants play a variant on the classic Prisoner’s Dilemma for large and widely ranging stakes averaging over $20,000. Cooperation is surprisingly high for amounts that would normally be considered consequential but look tiny in their current context, what we call a “big peanuts” phenomenon. Utilizing the prior interaction among contestants, we find evidence that people have reciprocal preferences. Surprisingly, there is little support for conditional cooperation in our sample. That is, players do not seem to be more likely to cooperate if their opponent might be expected to cooperate. Further, we replicate earlier findings that males are less cooperative than females, but this gender effect reverses for older contestants because men become increasingly cooperative as their age increases.

Dante said...

To the guy on the left, I would say "I like your method, I will chose the 'steal' ball."

I have to admit, I was surprised twice by the guy on the right. He either:

a) Did not care that much about the money and winning
b) Is quite confident in his ability to read people, and was willing to prove it on the air.

He strikes me as more interested in the game, so I think he did care about winning but is also quite confident in his ability to read people.

Well worth a watch!

Chip S. said...

This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma.

Um, that's what I said in my first comment.

bagoh20 said...

It does not matter what any player says, because the same set of possibilities are always in play, regardless. Just because he said he would steal does not mean that you can trust that he would, nor can you trust his promise to share it later. And in return, the guy on the right had no way to predict how the other guy will respond to his offer.

Consequently, the guy on the right changed nothing with his offer. They were both decent guys, and unless they knew each other, that was simple luck for them both.

Chip S. said...

Can announcements matter when they don't affect payoffs? That's the question behind the concept of cheap talk, which is totally useless in a game with a dominant-strategy equilibrium like the prisoner's dilemma, but not necessarily irrelevant when there are multiple equilibria, as in this case.

What's odd about this clip being labeled the best filmed example of game theory in action ever is that, in the game without side payments, there are three Nash equilibria--and none of them is the actual outcome of this game.

So either the clip provides some evidence against the usefulness of game theory, or else it's an illustration of how cheap talk can matter. The mystery to me is that Nic probably would have been more credible if he'd promised the other guy a much worse deal than 50/50. The guy is better off accepting a promise of, say, 10 pounds rather than getting zero (which is what he gets if they both "steal"), and Nic is more likely to actually follow through on a promise to pay 10 pounds rather than 6,000 or so. But any expected side-payment greater than zero is sufficient to induce Nic's opponent to choose "share" if he doesn't get pissed off enough to choose irrationally. Caveat: Strictly speaking, there's nothing in the payoff structure as defined by this game to give that result. It would be necessary to assign Nic a negative payoff from reneging on a very low-cost promise. But the main point is that it doesn't take very much faith that Nic will follow through at all to induce this outcome.

So I agree that it's ultimately about the individuals' personalities.

Tyrone Slothrop said...

The only Prisoner's Dilemma I'm familiar with is how to keep your pants up after they take away your belt.

Wince said...

Tyrone Slothrop said...
The only Prisoner's Dilemma I'm familiar with is how to keep your pants up after they take away your belt.

"Ben, nice to meet you."

Matt Sablan said...

That was awesome.

Synova said...

Ah, I see. The guy said he *absolutely* would choose steal, so that there was no motivation for the other guy to chose steal hoping he'd chose split. It was the best way to have control over both balls.

Not fool-proof, but still the closest to control over both that was possible.

Methadras said...

The advantage was with the fat guy. He initially said he was going to steal and that he would give his word to split the sum if the other guy chose split. He now has a 66% chance to win at that point because not only did he psychology psyche out the other guy, but he pushed the advantage towards him. The fact that he chose split is irrelevant since the stated outcome was the same. They split. 33% chance fat guy loses because bald guy was willing to sabotage the game and have them walk away with nothing, but the real lure is the advantage to walk away with something, rather than nothing and the psychological advantage that fat guy put on bald guy assured that he would get money regardless. Very interesting insight into human intuition however.