Prisoners and Their Dilemma

February 22, 2014 8:30 AM

What happens when you ask actual prisoners to test the "Prisoner's Dilemma"?

The paper is available here
NPR: The 'Prisoner's Dilemma' Tests Women In And Out Of Jail
American Scientist: New Dilemmas For The Prisoner

The Prisoner’s Dilemma has been a subject of inquiry for more than 60 years, not just by game theorists but also by psychologists, economists, political scientists, and evolutionary biologists. Yet the game has not given up all its secrets. A startling discovery last year revealed a whole new class of strategies, including some bizarre ones. For example, over a long series of games one player can unilaterally dictate the other player’s score (within a certain range). Or a crafty player can control the ratio of the two scores. But not all the new strategies are so manipulative; some are “generous” rules that elicit cooperation and thereby excel in an evolutionary context.

naked capitalism: Elinor Ostrom on the Prisoner’s Dilemma (Which You Should Approach with a Hermeneutic of Suspicion)

One important application of PD is found in Garrett Hardin’s extremely influential “Tragedy of the Commons” (Science162, 1243-1248 (1968)):
...
(Hardin, though citing to game theory sources, does not use the term PD explicitly. However, the payoff matrix for cooperation vs. defection is the same, as is the outcome of the game.) QED, right? Not so fast.
It’s interesting to note that when social scientist got around to — quelle horreur — actually testing Prisoner’s Dilemma on real prisoners, PD (and by extension not only Tucker’s thesis, but Hardin’s “tragedy”) broke down:

posted by the man of twists and turns (32 comments total)

Note that "in non-iterated PD, actual prisoners are more likely to cooperate than non-prisoners" was also the conclusion that The Dark Knight came to.
posted by baf at 8:43 AM on February 22, 2014 [17 favorites]

Maybe their tendency to cooperate is the real reason we lock them up.
posted by Obscure Reference at 8:58 AM on February 22, 2014 [5 favorites]

Cooperation in prison is brutally enforced. If it gets back to the group that one defected to the screws there would be hell to pay. It's not surprising that more prisoners decided to cooperate with their fellow prisoner.
posted by Talez at 9:15 AM on February 22, 2014 [2 favorites]

Its not a "real" Prisoner's Dilemma unless the 'prize' is to avoid prison. Still, interesting research.
posted by memebake at 9:16 AM on February 22, 2014 [3 favorites]

These are young women in a German prison which looks pretty civilised, really. So it's worth remembering that the level of brutality may be lower than the typical person reading here imagines.
posted by ambrosen at 9:17 AM on February 22, 2014 [1 favorite]

This is fascinating. Reminds me of this, which I'm pretty sure was an earlier FPP.

Its not a "real" Prisoner's Dilemma unless the 'prize' is to avoid prison.

Apologies if I missed your hamburger tag, but if you're talking economics, sure it is. All you need is sufficient incentive to screw the other party over, or 'suboptimal Nash Equilibrium.' I mean, it's not like economists were literally talking about prisoners all this time - per the article, actually talking to prisoners was considered a lark.

It's just a peek at why people fail to cooperate, mostly relevant so you can discuss how to deal with that. (Iteration? Add punishments? Etc.)

Also, I'm not at all surprised students defect more than prisoners. Being a student is mostly about resenting cooperation - group projects are an attempt to get you used to playing nicely with your peers, but they mostly have the opposite effect. The other participant isn't your buddy, they're probably a millstone. (Ironically, the only place that wasn't true when I was going to college? Game theory. Sharp folks in there.)

Being a prisoner is a whole different world, where cooperation is (as mentioned above) a survival skill. I mean, even if you're in a place where you're not going to get a shiv in the back, it's still a really small world - it's always important to be a team player if you can't quit the team.
posted by mordax at 9:57 AM on February 22, 2014 [5 favorites]

it's always important to be a team player if you can't quit the team.

This is why offering actual prisoners freedom from prison (a/k/a a chance to quit the team) has the potential to change the dynamics considerably as compared to any other "suboptimal Nash Equilibrium".

Still, interesting article.
posted by mstokes650 at 10:02 AM on February 22, 2014 [2 favorites]

For the Freakonomics fans, here's a correlation: when other sociodemographic variables were controlled, the only factor that correlated with cooperation was coffee drinking.

This is of course, AFTER they are given coffee OR during the process of getting the pot ready for brewing... before that point... not so much.
posted by Nanukthedog at 10:03 AM on February 22, 2014 [2 favorites]

On this morning's CarTalk rerun, they had this puzzler going
posted by growabrain at 10:07 AM on February 22, 2014 [1 favorite]

Interesting article, but I don't think it really tested the Prisoner's Dilemma due to the lack of real consequences. If someone picks up on this and decides to test the Pirate Game with real pirates, make sure you give them a floatation device when you throw them overboard.
posted by klausman at 10:58 AM on February 22, 2014

I can't read "Nash Equilibrium" without thinking of comic verse about gun kata.
posted by Mr. Bad Example at 11:19 AM on February 22, 2014 [1 favorite]

Ah, my great-great-great-...-great-grandfather Garrett Hardin. I share his enthusiasm for game theory, though where he preferred to theorize, I prefer to win the game.
posted by Salvor Hardin at 12:13 PM on February 22, 2014 [1 favorite]

The Elinor Ostrom bit is *crazy* insightful.

What she says, if I understand it, is that the Prisoner's Dilemma is how one group of people imagines a second group of people as essentially automatons who act in ways completely prescribed by their situation, and are unable to change their situation or reason their way around it or create structures to compensate for and improve their situation.

Then the first group of people thinks of ways to change the second group's situation, reason around it, or create structures to compensate for and improve the second group's situation.

The first group are usually economists who are, or are trying to be, in a position to influence public policy, the second group are the rest of us schmucks.

...

It has always struck me as amazing that people are willing to model situations in terms of "the Tragedy of the Commons," which is an proof that it is economically impossible to hold land in common, which is something which people in fact DID for the entire middle ages, until the Enclosure movement privatized everything. As far as I'm concerned, when your model is contradicted by a thousand years of reality, you discard it. But I guess when your model says that socialism is impossible, it's more precious than reality.
posted by edheil at 12:22 PM on February 22, 2014 [15 favorites]

The thing that jumped out at me here from the article was that the payoffs in the game were in "points," not (even small amounts of) money or other useful stuff.

So there's a bunch of different ways you could describe the result. One is "Prisoners are more cooperative than psych undergrads." One is "Psych undergrads are more motivated than prisoners by the prospect of earning abstract 'points' with no real-world value."
posted by this is a thing at 12:26 PM on February 22, 2014 [2 favorites]

I like the way that an article about female prisoners in a low-security prison is illustrated by a photo of a man with heavy tattoos in handcuffs. I call this "The Newspaper Editor's Dilemma."
posted by GenjiandProust at 12:28 PM on February 22, 2014 [8 favorites]

this is a thing: it's kinda buried in the article, but they could trade the points for money. Still, would be interesting to see if the results were different if the stakes were higher (actual time off sentence, as per the original Dilemma).
posted by Pink Frost at 12:37 PM on February 22, 2014 [2 favorites]

Well, the scenario that goes "Okay these two criminals get arrested...." isn't actually an essential part of the Prisoner's Dilemma game. That scenario is basically just a cute mnemonic device and teaching tool. Any situation with the right payoff structure counts as a Prisoner's Dilemma.

But yeah, in real life people do behave differently in situations like these depending on how much is at stake. I'm sure you could induce more of the prisoners to defect rather than cooperate if the payoffs were valuable enough.
posted by this is a thing at 12:50 PM on February 22, 2014 [1 favorite]

It has always struck me as amazing that people are willing to model situations in terms of "the Tragedy of the Commons," which is an proof that it is economically impossible to hold land in common, which is something which people in fact DID for the entire middle ages, until the Enclosure movement privatized everything.

It's a really useful tool that still does a lot of good work today. It's just that it applies less and less the more people have to actually live close to their consequences while making the same choices. Just like the Prisoner's Dilemma the purest form of it has the actors acting only once, and just like the Prisoner's Dilemma that often doesn't apply well to the real world.

But you only need to look at something like twitch.tv does pokemon to see that it's a good model. Elinor Ostrom did not disprove the tragedy of the commons, she demonstrated qualifications.
posted by tychotesla at 1:03 PM on February 22, 2014 [1 favorite]

Any situation with the right payoff structure counts as a Prisoner's Dilemma.

That may be a problem. Game theory operates at a very high level of abstraction and payoffs other than points may matter here. For example, pride matters to people. Part of the payoff of defecting in this game is the shame you'd feel at being petty enough to scam someone for a few points in a dumb game, or scam someone for a few bucks.
posted by justsomebodythatyouusedtoknow at 1:06 PM on February 22, 2014

One lesson: don't trust anyone who won't sit down for a cup of coffee.
posted by john wilkins at 2:00 PM on February 22, 2014 [1 favorite]

As far as I'm concerned, when your model is contradicted by a thousand years of reality, you discard it.

The tragedy of the commons demonstrates that there are situations where rational self-interest produces sub-optimal results for everyone in the long run, not that "it is economically impossible to hold land in common". It's easy to hold land in common - you set up a structure that imposes external costs to discourage what would otherwise be rational self-interested actions.

But hey, I guess "lol economics" reads better.
posted by kithrater at 2:22 PM on February 22, 2014 [5 favorites]

The PD as laid out in the Ostrom piece:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. Each prisoner is given the opportunity either to betray the other, by testifying that the other committed the crime, or to cooperate with the other by remaining silent. Here’s how it goes:

• If A and B both betray the other, each of them serves 2 years in prison
• If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
• If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)

It’s implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision won’t affect their reputation in future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other.

Anybody I would even begin to consider accepting as a member of my criminal gang would be sharp enough to realize, once advised of the "A betrays B but B remains silent" outcome, that the same deal was being offered to both of us, that both of us - being equally rational - would therefore make the same choice, and that of the two ways that could happen, the one with the best payoff is remaining silent.

Then again, I've spent years taking low doses of iocaine.
posted by flabdablet at 6:12 PM on February 22, 2014 [2 favorites]

I remember reading in college (a million years ago) about an experiment where an iterated PD tournament was set up and academics were invited to submit computer programs to play a tournament. The winning strategy was TIT-FOR-TAT, which cooperated on the first round then repeated the other player's move from the previous round back on each subsequent round. This strategy is interesting because it's altruistic (it will continue to keep mum for the entire game so long as the other player does) and forgiving (it returns to keeping mum if the other player does) but also vengeful (it immediately retaliates for bad behavior on the other player's part -- here 'bad behavior' means 'betrayal').

I always thought this was interesting because if you apply it to career criminals, it explains why snitches are reviled. They're playing the game badly, because everyone's much better off keeping mum.
posted by axiom at 7:25 PM on February 22, 2014 [1 favorite]

The tragedy of the commons demonstrates that there are situations where rational self-interest produces sub-optimal results for everyone in the long run, not that "it is economically impossible to hold land in common".

Doesn't this pretty much undercut the idea of "rational" in the term "rational self-interest?"
posted by GenjiandProust at 3:32 AM on February 23, 2014

Game theory is all about the kind of rationality that proceeds from an assumption of pure self-interest. My gang and I are, of course, superrational.

The Prisoner's Dilemma is more about the limitations of game theory as a tool for understanding real human behavior than about prisoners. The existence of governments and regulators and gentlemen's agreements demonstrates that superrationality, or something rather like it, does in fact influence the real world in ways that game-theoretic rationality does not explain well.

Game theory is really, really good at predicting the behavior of agents lacking a theory of mind.
posted by flabdablet at 3:53 AM on February 23, 2014

I always thought this was interesting because if you apply it to career criminals, it explains why snitches are reviled. They're playing the game badly, because everyone's much better off keeping mum.

You don't actually need to iterate if you have the ability to think about what other people are doing or will do; massively parallel concurrent execution gives you equivalent results more quickly.
posted by flabdablet at 3:57 AM on February 23, 2014

Doesn't this pretty much undercut the idea of "rational" in the term "rational self-interest?"

It depends. Rationality as per ratioal choice theory is a slippery concept. Solutions/responses to the tragedy of the commons come from inside and outside the rational actor framework. To make things easier, insert "short-term" before "rational self-interest".
posted by kithrater at 4:51 AM on February 23, 2014

Not really... in game theory, all it means is that higher payoffs are better. There's no substantive content to it, and you can work in any substantive definition of 'rationality' you like into any game you want by specifying the correct payoff structure.

More broadly, all the rationality of rat choice implies is goal oriented behavior. There's nothing about short or long term, or having or lacking a theory of mind , that's part of rationality. That's all part of correctly defining the strategic interaction and payoffs for whatever you have in mind.
posted by ROU_Xenophobe at 7:06 AM on February 23, 2014

But the PD as presented above shows that to maximize your payoff you do need a theory of mind; you need to understand that your opponent is faced with the same payoff matrix as you are and will therefore, given only that they are as rational as you, make the same choice you do.

Attempting to compute an expected payoff for defection while treating the opponent's choice as unknowable - perhaps as an average between the defect/cooperate outcome and the defect/defect outcome - just doesn't work. You both end up defecting, so you both lose. That's kind of the point of the PD thought experiment.

But if you apply superrationality, which necessarily does involve taking into account your opponent's nature as a similarly rational actor, then the defect/cooperate and cooperate/defect outcomes are both immediately out of the question, and cooperate/cooperate is clearly the winning move from those remaining available.
posted by flabdablet at 8:26 AM on February 23, 2014 [1 favorite]

No, all you need to do to deal with the situation you describe is change the payoffs so there's a single pareto optimal nash equilibrium. At which point nobody will recognize it as a pd game anymore, but the strategic situation will be the one you want to model.

Tl,dr: you're mostly arguing that the 'real world' situation usually encoded as the pd game should instead be encoded as soke sort of coordination game.
posted by ROU_Xenophobe at 9:08 AM on February 23, 2014 [1 favorite]

How you encode these games is everything, really. Change the language you use to describe them, and you will change the outcome.
posted by lodurr at 3:22 PM on February 23, 2014

From the NPR story linked in the FP:

In fact, looking more closely at the data, there was no difference in the rate at which prisoners and students cooperated when averaged across responses to the simultaneous dilemmas and Round 1 of the sequential dilemmas — where the only difference is whether the person anticipates that her partner will know her choice before choosing herself.

The authors of the original research don't hide the fact that their primary group differences don't meet the .05 criterion for significance, though they do go on to draw conclusions from the marginal results. In some ways this is reasonable — their sample size wasn't huge (90 prisoners, 92 students), which limited their statistical power; the prison population isn't easy to access for this kind of research, so they couldn't have readily boosted their sample size. Weak evidence is still better than no evidence.

Reports in the popular press, however, have not been very cautious. You wouldn't know from the LA Times report, the Business Insider story, or the Smithsonian.com blog post, for example, that the reported group differences are so shaky. One (otherwise lovely) report states that the prisoners "betray one another far less than college students do" (emphasis added), when in fact — by standard conventions in psychology — all we should conclude is that we lack strong evidence for a difference between the two groups.

... which seems to be saying that there's actually no there, there.
posted by lodurr at 6:22 PM on February 23, 2014 [1 favorite]