Study: Actual Prisoners Better Than You at Solving Prisoner's Dilemma

prisoner's dilemmaCredit: Walt Stoneburner / photo on flickrYou've probably heard of the prisoner's dilemma. It's a hypothetical used to teach basic game theory in introductory econ. It goes like this

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. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch...If both prisoners testify against each other, both will be sentenced to two years in jail.

The best outcome overall is for both players to remain tightlipped, but the dominant strategy for any individual player of the game is to rat your partner out, which increases your chance of a better outcome.

This classic thought experiment about cooperation and defection has occasioned the spillage of much academic ink, and econ and psychology grad students are constantly subjecting each other to lab experiments on this theme, but no one seems to have thought to try it on actual prisoners until economists Menusch Khadjavi and Andreas Lange of University of Hamburg conducted that experiment and published a study about it this year.

Since University of Hamburg economists lack the authority to actually imprison their test subjects (so far!), the payoffs were in coffee and cigarettes for the prisoners at Lower Saxony's primary women's prison and equivalent amounts of cash for the control group of students. 

Prisoners, it turns out, were significantly more likely to cooperate in the classic version of the game, where the two players must make their decisions simultaneously: 56 percent of inmates refused to squeal, compared with 37 percent of students. Only 13 percent of student pairs managed to get the best mutual outcome, compared with 30 percent of prisoner pairs.

The Business Insider writeup of the study included this possible explanation for the discrepancy: 

Perhaps prisoners are much more familiar with the high successful "Stop Snitchin" campaign, than they are with John Nash's game theory.

Editor's Note: We invite comments and request that they be civil and on-topic. We do not moderate or assume any responsibility for comments, which are owned by the readers who post them. Comments do not represent the views of Reason.com or Reason Foundation. We reserve the right to delete any comment for any reason at any time. Report abuses.

  • ||

    Hmm, maybe if students learned the hard way that snitches get stitches they'd be better at game theory.

  • SugarFree||

    And yet people got all pissed off when they found I was putting stray cats in boxes with fragile bottles of poison, hammers, and fancy isotopes.

  • Paul.||

    Was Schrödinger pissed off that you had his cat?

    And have you ever been to a fancy isotope party?

  • Bardas Phocas||

    We had rainbow isotope parties when I was a teenager.
    yeah, it got burn't.

  • SugarFree||

    Schrödinger? Who's that?

  • ||

    He's the guy standing right there.

  • Eduard van Haalen||

    True story: I adopted a stray cat and called him Schrödinger. Bad idea - he walked away and I haven't seen him since.

  • Sevo||

    Have you opened every box in the house?

  • ||

    The world is (or isn't) his box, now.

  • Paul.||

    Have you opened every box in the house?

    At the same time?

  • Hugh Akston||

    He may or may not be in the room you're not in.

  • Eduard van Haalen||

    Now you'll have me looking over my shoulder all the time.

    My next cat will be called Inertia.

  • Killazontherun||

    I didn't care for the nephew naming one of our kittens Shaggy, but he's living up to that name. The cat is a total dope. He likes to jump on top of his food, spread it out, and then rake it back together before eating it.

  • Eduard van Haalen||

    Do he and Scooby get along?

  • Killazontherun||

    Shaggy came up to me as I was feeding him and said, 'the fucking dog talks, mannnn!'

  • Agammamon||

    Why do you hate God so much?

  • OldMexican||

    The Business Insider writeup of the study included this possible explanation for the discrepancy:

    Perhaps prisoners are much more familiar with the high successful "Stop Snitchin" campaign, than they are with John Nash's game theory.


    Or perhaps the case is that game theory is just pure and unadulterated bullshit, completely and totally unsuited to understand real economic phenomena, as we're dealing with rational, acting humans with preferences and not robots.

  • ||

    Thanks for your input. We all really appreciate it.

  • Tonio||

    Or perhaps game theory is valid, but just uses bad examples. You could easily redo the prisoners dilemma using two people who have knowledge wanted by a third person where nobody was a prisoner. Wouldn't be as accessible, or have as catchy a name, as prisoner's dilemma, but would still be a valid situation.

    Yes, the snitching thing is a problem when the two people with knowledge are actual prisoners.

  • Killazontherun||

    It's better applied to sociology where you may want to develop a model of human interaction to compare different cultures to a neutral optimum value. In economics, game theory is a distraction.

  • Brandybuck||

    In its pure form it's just a logic puzzle. Specific individuals do not behave this way 100% of the time. Yet in aggregate humans do tend towards Pareto optimality (but never reaching it). This does not mean game theory is bullshit, just that it does not universally predict an individuals behavior.

    A related example is the supply and demand curve that every economist accepts. It's based on a game theory like premise of marginal utility. As an OldAustrian you should be aware of this. But a nice smooth demand curve cannot definitively predict any single individual's price preference. It's only in aggregate that a demand curve makes sense. Yet this doesn't mean that marginal utility is bullshit.

  • OldMexican||

    Re: Brandybuck,

    It's only in aggregate that a demand curve makes sense. Yet this doesn't mean that marginal utility is bullshit.


    The problem with your comparison is that Marginal Utility is not a concept based on continuous values but on cardinal values which are themselves based on a person's subjective preference. Indeed, a price is the aggregate of the end result of market clearing, that is the effect of thousands or millions of trade interactions reaching an equilibrium, however always known after-the-fact, that is after humans have shown their preferences and not before.

    Instead, Game Theory is entirely based on predetermined outcomes, and the bullshit part manifests itself after sociologists and other mountebanks pretend that the results are justification for prescribed normatives, or tyranny (to put it more succinctly.)

  • Anonymous Coward||

    The problem with the prisoner's dilemma is that it doesn't take into consideration just how potentially dangerous it is testify against your co-conspirator in a felony.

    You testify, he gets three years, who do think he's going to look for as soon as he hits the streets?

  • Tonio||

    Doesn't even have to wait for that. Prisoners get murdered in prison on the orders of other current/former prisoners.

  • Hugh Akston||

    It doesn't surprise me. College students are notoriously ignorant of basic knowledge like how to structure a paper and "never ever ever ever talk to the cops."

  • Paul.||

    56 percent of inmates refused to squeal, compared with 37 percent of students

    In prison, there are consequences to squealing.

  • Floridian||

    It was a women's prison. What are they in for, shop lifting shoes? I doubt the consequences are that severe for squealing in a women's pen. They gossip all the time anyways.

  • Paul.||

    They'll be denied hot lesbian action!

    Or, wait, I'll be denied hot lesbian action!

  • Anonymous Coward||

    36 percent of women in prison are inside for violent crimes.

    There are a few bitches in there who will gladly bash your skull in.

  • ||

    All of you bitching about game theory are wrong; it's not the game theory that's wrong, it's the (real) perceived payoffs for different strategies. In the real world the pay off matrix isn't what academics think it should be. That doesn't invalidate the theory for how things should work when the pay offs are known with certainty.

  • Tonio||

    ^This. Very succinctly put.

  • Rasilio||

    But that flaw is present in virtually every game theory scenario I have encountered. It works just grand in a lab scenario where variables are intentionally limited but is worth shit when you try to extrapolate to the real world because there are an infinite number of incentive matrices.

    I cannot count the number of times that I have seen social scientists put out papers questioning peoples rationality because their choices did not match the game theory optimal outcome while completely ignoring the fact that those individuals are not bound to the same limited preference matrix offered in the game

  • Stormy Dragon||

    Prisoners, it turns out, were significantly more likely to cooperate in the classic version of the game, where the two players must make their decisions simultaneously: 56 percent of inmates refused to squeal, compared with 37 percent of students. Only 13 percent of student pairs managed to get the best mutual outcome, compared with 30 percent of prisoner pairs.

    Probably because the college students weren't afraid of getting shivved in the dorm shower because their counterparty was upset about losing cigarettes in that experiment thing last week.

  • Mendelism||

    Wait, isn't the point of the prisoner's dilemma that ratting out the other person has the higher expected value? So the headline has it backwards, no?

  • Mendelism||

    In fact couldn't the difference in results be explained by the university students having been exposed at a greater rate to game theory, and this game in particular?

  • ||

    FTA:

    The four sessions with student subjects were conducted in the experimental economic laboratory of the School of Economics, Business, and Social Sciences at the University of Hamburg about three weeks later, in the first week of July, 2012. Female students were recruited via ORSEE (Greiner, 2004) from the subject pool which comprises students of different majors. In order to allow a better comparison with inmates, we also recruited a significant number of student subject who were relatively new to the subject pool and had therefore less (or no) experience with lab experiments. Similar to the inmates in the lab-in-the-field setting, student subjects received information that they can receive earnings by making anonymous decisions on computer terminals. The payment vehicle for student subjects was the usual: a sum of cash consisting of a 5-EUR show-up fee and money determined by decision made in the experiment.
  • robc||

    Except when both rat.

    So if both figure it out, they both go down.

    So "winning" is not snitching.

  • ||

    Sure, but that means each actor choosing the individually rational option results in the worst outcome for both.

    So the headline is right.

  • ||

    I think this aspect of the outcome is more interesting:

    On average, prisoners behave more cooperatively than students in a simultaneous Prisoner's Dilemma. Conversely, student first movers in the sequential Prisoner's Dilemma are more likely to cooperate than inmates in this position.
  • ||

    As other have point out, the game plays out differently in real life than in the classroom. In real life, the one snitching, unless given witness protection can fully expect swift retribution.

    It's comparing apples to banana.

  • ||

    Maybe I wasn't clear; what I find interesting about the outcome is that it's reversed for sequential games.

  • Eduard van Haalen||

    "Yeah, your buddy already admitted he was in on the robbery, and he says you were the ringleader. Also, he says you smell."

  • Invisible Finger||

    So we have a study with the "success" rate for actual prisoners and college students.

    I wonder what the rate would be for, instead of college students, two police officers accused of corruption.

GET REASON MAGAZINE

Get Reason's print or digital edition before it’s posted online

  • Video Game Nation: How gaming is making America freer – and more fun.
  • Matt Welch: How the left turned against free speech.
  • Nothing Left to Cut? Congress can’t live within their means.
  • And much more.

SUBSCRIBE

advertisement