The Prisoners’ Dilemma

A post by The Daily G  the other day on cooperation and competition reminded me of The Prisoners’ Dilemma.

If you aren’t familiar with this, it’s a game theory developed in 1950 by a couple of math guys working at RAND  It gives players the option of cooperation or defection.  It’s a puzzle that, 60 years later, continues to be studied by philosophers, biologists, sociologists and politics (And bloggers, of course).

Prisoners’ Dilemma models have been applied to almost every form of human and animal interaction. Well-known examples from politics include arms races, income policies, trade bargaining, pollution reduction and exploitation of natural resources.

I don’t want to get into the complexities of game theory as a whole – mainly because I don’t understand it, and probably math geeks, game theory geeks, philosophers and all sorts of other people will be rolling over in their graves and laboratories at the mess I will make in talking about this. However,  I think the Prisoners’ Dilemma is interesting to think about on its own and perhaps as a model for examples of cooperative behaviour on individual levels.

The Prisoners’ Dilemma, as formalized by Albert W. Tucker goes like this:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated the prisoners, visit each of them to offer the same deal. If one testifies for the prosecution against the other (defects) and the other remains silent (cooperates), the defector goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?

 What would you do?

  • If you confess and your accomplice remains silent, you go free and your accomplice goes to prison for ten years.
  • If your accomplice confesses and you remain silent, you go to prison for ten years and your accomplice goes free.
  • If you both confess you will both serve five years.
  • If you both remain silent, you both go to prison for six months.

Your first reaction is probably to say that you should both just keep your mouths shut (cooperate) and serve only six months in jail — the best possible solution for everyone.

 But then you have to hope that your accomplice is thinking the same thing or you’ll end up spending 10 years in jail. Neither of you can rationally depend on the other to keep his mouth shut, so both of you have no choice but to defect/confess and go to jail for five years — even though cooperating would have been in your best interests.

You have made a decision that goes against your own best interests because it’s impossible for you to reach a rational cooperative solution.

It’s apparently almost impossible to get rational, selfish beings to cooperate for their common good.

This conclusion has astonished and dismayed social scientists because it seems to mean there is a fundamental flaw in the social fabric. People will not cooperate, even if it’s in their best interests to do so, because individual incentive trumps the collective incentive. This would sort of mean that we are hopeless as a species, wouldn’t it?

A lot has been written to refute what has been cited as the only possible solution to the Prisoners’ Dilemma. But I don’t know. Cooperation requires a great deal of knowledge of, and trust for the other person/group. And trust isn’t rational.

Anyway, I thought this would be something interesting to puzzle over and discuss during the weekend.

I wonder if we can come up with Prisoners’ Dilemma situations in our every day life that either prove or disprove the rational impossibility of cooperation?


33 responses to “The Prisoners’ Dilemma

  1. Well this points to something I’ve been saying for maybe 30 years: You can never truly know another person’s mind. That’s an absolute fact. Taking that fact into consideration, why take the chance on the 10 years?

  2. You’d be looking at five years in prison. The rational conclusion about an irrational situation is that your accomplice will do what’s best for him: confess.

    You would have to confess as well, hence you’d both end up serving 5 years. (Kind of a variation on the lesser of two evils.)

    As for everyday life… The closest I could think of would be a work group/team in your workplace. You know that a few of you will get some recognition for the work the group does, and perhaps get promoted.

    You could try to sabotage the work, but then no one would get promoted, including yourself. You could help, but you might still not get promoted. You could help and no one gets promoted.

    You take a risk no matter what choice you make.

  3. Gosh, I have no idea. I’m horrible at things like this. I’m too naive and trusting and would probably think the other person would keep their mouth shut.

  4. If they are guilty, then the best choice would be for both to admit it.

    However, if one assumes that all they are guilty of is the lesser charge, then that’s all they should admit to.

  5. I think that life experience has taught us that all humans are inherently selfish. In fact evolutionists would have us believe in the selfish gene, which is that our first priority will always to ensure our genetic material has the best chance of surviving and multiplying. Hence, I applaud the ideal that both will remain silent but won’t take the chance and will sing like a canary.

  6. In this dilemma, betrayal is the lowest overall risk and thus the more rational decision.

    If you assume that both guys really are guilty and both rationally minded, and ignore idiosyncracies in the legal system (i.e. assume the legal system is actually fair and never makes mistakes), then you can weight the decisions sort of like this:

    Keeping silent: 50% of 6 months in jail plus 50% of 10 years in jail = 63 months in jail

    Betrayal: 50% of 5 years in jail plus 50% of freedom = 30 months in jail

    Betrayal is a much lower personal risk, even if it doesn’t necessarily generate the best outcome. In fact, it’s also the only way of generating the best individual outcome. It’s a risk management behaviour that probably comes out of our deepest emotions. To choose to keep silent in this situation would require a lot of high-functioning thinking that you’d have to be damn sure the other person is also capable of.

    When you throw in the realities of the legal system, however, both keeping silent is almost certainly the better choice, although it’s still riskier. In Canada, it’s going to take more than 3 months to go to trial, and as is evident, both people are already in custody. There’s little to lose by both shutting up since they’re going to be in jail anyway and they’d be sentenced to time served, probably with 2:1 credit, so they walk out free at the end of the trial. The “freedom” becomes “lack of a conviction record” and is harder to weigh to assess risk for the dilemma. Although in personal risk, betrayal is still the lowest risk option if all other things are equal, the legal system makes a shortcut to an optimal solution.

  7. I predict these are topics that will be covered in today’s comment thread.

    1. If we learned to think of others beyond ourselves, everyone would benefit in the long run.

    2. The West is selfish and that’s the reason our planet it in trouble.

    3. This is like the Third World, except we are the ones who get off free, and they’re the ones sentenced to a live of poverty.

    4. Our legal system is broken and our prisons are overcrowded.

    5. We should focus less on punishing criminals and more on fixing the root cause of crime.

    I’m not saying these statements are wrong. I’m just saying that this is how I think the comment thread will go.

    As for myself, I have nothing original to add here. (It will all have been said!) 🙂

  8. I’m all for cooperation, but anyone (human or not) is out to survive and do the best they can in a bad situation. Logically, you talk and hope the other guy is an idiot (ok, the other guy is a good and loyal and ethical person, i.e., in this case an idiot) and shuts the hell up.

  9. XUP, ‘The Prisoner’s Dilemma’ was indeed developed by the RAND corporation, which was a private think-tank tasked with out-gaming the Soviets in the nuclear arms-race. Their ideas went on to influence political thinking in all areas.

    It was not known at the time that the main man behind the theory was a paranoid schizophrenic. Professor Nash believed that everyone wearing a red tie was a communist sent to spy on him. He was diagnosed only years later and has been in treatment ever since.

    It is not widely known that RAND’s own experiments never verified their conclusions. Whenever they tried to demonstrate game theory in action with human subjects, they would cooperate instead of betraying each other.

    The only people who did behave like their game-theory models were themselves, the economists, and psychopaths.

    Yet everyone simply takes this version of human nature on faith because it comes from an authoritative source.

    Here is an excellent BBC documentary all about it:

    (Scroll to the bottom of the text; the three parts are pasted in descending order.)

  10. I’d worry about myself and not what the other person would do. I would confess; couldn’t live with myself if I didn’t. I’d risk having to go to jail for 5 years (I’d be guilty, after all). It’s at least better than 10 years and if my darling partner kept their mouth shut, well then… I’d be home free.

    In the case of everyday life, this sounds a lot like defensive driving. Seems necessary to consider what the other one might do when roaming through the jungle of life. And… er… maybe even save one another from landing in this sort of situation to begin with 🙂

  11. I preferred the game where you roll dice and land on various properties, you acquire said properties, and if you are smart you are soon a slum lord and take advantage of the poor starving masses.
    I believe it was called “Communism”

  12. Geewits – That’s I guess what all the game theorists decided too. It does say something rather profound about human beings and their inabilility to work together for the common good, doesn’t it?

    Ken – Ya, I was thinking of a work team as well. If the project could mean the end of or kick-start to your career, you’d have to make damn sure the thing gets done on time, and as perfectly as possible. And the only way you could be sure of that would be to do it yourself, even if that means working day and night for weeks or months. Because when have you ever been able to trust your entire team to do what they’re supposed to do??

    Linda – Ten years in the slammer for you! Would you really trust your accomplice so much that you’d gamble 5 years of your life in hopes that he/she also stays silent?

    Monkey – I hope you and Linda rob the bank together. Then you’d both stay quiet and get out of jail in 6 months. You are surprisingly trusting for a guy with a history like yours. Good for you!

    Mike – There is no lesser or greater charge to admit to — they either confess or they don’t. They get 6 months each if they both stay quiet or 5 years if they both confess. If only one of them confesses, the one who didn’t confess gets 10 years and the one who did confess gets 5 years.

    LGS – What does that mean for human beings though? Will we always be working against our better interests? Is there no way for humankind to work cooperatively toward a common good? In the case of these criminals, even if they had a chance to confer beforehand and discuss what they were going to do and they agreed to stay silent…would they trust each other to keep to the agreement, knowing that if one of them talks the other will face 10 years in jail?

    Squid – It’s not meant to be a legal puzzle – more of a strategy/cooperation puzzle. Did your kids every play one of those stupid coopertive board games? I’ve never seen children actually enjoy them. They always want to know who’s winning and are really disappointed when everything is always equal.I think competition is a basic, inherent human trait. We are programmed to mistrust, to best the next guy. It’s a survival thing I guess and I suppose it works better than coopertion would maybe???

    Friar – Well, I hope you’re wrong because that’s not really what this dilemma thing is all about.

    Jazz – So you’re agreeing that survival, by necessity is ugly, and that we can’t afford to be nice and trusting or we’ll go down?

    Milan – Yes. As usual, you explain it very well. The depletion of all natural resources fits the prisoners’ dilemma model

    G. – I read that it was about half and half on who defected and who cooperated. But the people who cooperated were not necessarily doing so for rational reasons. As you can see from the comments, a few people said they would keep their mouths shut, too and get the 6 months. I don’t know if that speaks any better for the human race since they would be guilty people trying to get away with something.

    Davina – The only logical thing to do is to confess, I think…whether you’re thinking about what the other guy is going to do or not. Defensive driving is a good example, as is security in your home. You’re making yourself something of a prisoner in your house with locks and gates and alarm systems because you can’t trust others not to break in and steal your stuff or kill you in your sleep.

    Lebowski – Are you sure that isn’t capitalism? Anyway, you can’t just go around changing the game because you don’t want to play the game we’re all playing. So there!

  13. XUP, that documentary is really worth watching.

    Life is not a game; it can’t be reduced like that. It can’t be modelled. Game theory as applied to human behaviour comes out of Cold War paranoia and people comform to it the more they believe in it, just like Christians will (sometimes) behave in Christian ways, etc.

  14. I realize it’s not intended to be a legal puzzle, but it is a dilemma and the players have to have a process to arrive at a solution.

    Since they can’t communicate with each other to ensure the optimal solution, they have to think rationally and assess personal risk. Even if you don’t attach numbers to it, you have to assume if the other guy is as smart as you, he will come to the same conclusion and shaft you. If you think he’s a cuddly type, it’s still worth it to shaft him depending on what you think of him. Only if you’re absolutely certain that both of you are total cuddle-bunnies would it be worth it to keep quiet… and if you were both cuddle-bunnies, you wouldn’t be on your way to a criminal trial in the first place 🙂

    The lowest personal risk is to blade the other guy. It’s quite straightforward really.

  15. Guys, guys, guys, you are being suckered into a very dark worldview spun by Cold War paranoiacs. Life is not like the Prisoner’s Dilemma except in a few unfortunate situations that are created by people who do think like this. Cut-throat businessmen, ruthless military-men, and jealous politicians do think like this, as well as psychopaths. Do not let them set the tone for the entire human race, please. Game Theory is useful in its place, but it is sort of idolatrous to think that it fully describes reality, and is certainly reductive.

    There’s always a Model of the Moment that future generations look back at and laugh.

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  17. Friar – True. But that’s sort of the fun of the whole thing, isn’t it?

    Sean – Ah, you’ve used it with your classes then?

    Squid – I think that’s pretty much what most people have decided, although I understand there’s a novel by the same name that tries to refute the logical conclusion.

    G – I’m sorry you don’t approve of this topic for blog discussion and that I haven’t presented it a suitably responsible and scholarly manner.

    Nat – ha ha…I don’t think lawyer was part of the option, for some reason.

  18. An extended miniseries on NBC just came to an end, called “Persons Unknown”.

    I think the creator must have thought about this dilemma because the basis of the show is somewhat similar: People have been captured, put into an environment with no direction. Do they co-operate to try and figure out what’s going and get out, or do they follow cryptic instructions like “Kill your neighbour and you’ll go free”?

    Eventually they figure out how to work together, but not before letting a whole lot of mistrust and paranoia to creep in.

    And from the looks of it, the dilemma presents the same question: do you trust other people and let them help, or do accept the paranoia that people are out to get you and you do what’s best for yourself?

  19. XUP, you have no cause to take anything personally in what I’m saying. I am concerned with shooting down the idea, not you. The idea is poison because it takes a very limited, static situation and uses it to make sweeping generalisations about life, which does not truly resemble the model.

    In your write-up here you describe the experiment and then suddenly jump to this conclusion, which appears to be your own point of view:

    “It’s apparently almost impossible to get rational, selfish beings to cooperate for their common good.”

    This is not only wrong; it’s obviously wrong as it contradicts empirical evidence in everyday life. But if a model convinces you to see only selfishness, you will look around the real world and see only selfishness. This is my concern. It is a legitimate, altruistic concern and not a selfish attempt to steal the thunder of another blogger, if that’s what you’re worried about. I don’t know.

    The game is fixed: it predetermines the response with its initial conditions. In real life, people go to the gallows for honour, vanity, altruism – all sorts of reasons. This happens less when people live in an ideologically neutered world that is only about consumerism and which fears those who truly believe in something substantial. This neutered world is the world created by people like the RAND corporation, who actually believe that everyone must act selfishly in order for society to work. That is not a misrepresentation, look it up. They think good comes of evil; it’s madness.

    Adam Smith never had this in mind. It’s a worldview that comes from fringe crackpots who had their day in the spotlight just when American leaders had a phantom war of second-guessing to win.

  20. Ken – Well, I did read that this puzzle has been used in a many different ways for a many different situations – novels have been written based on this; there was a Dr. Who thing based on I wouldn’t be a bit surprised if Persons Unknown were based on it as well.

    G – I’m not taking it personally. I’m sincerely apologizing because this blog isn’t up to the standard of your blog. I don’t pretend to write definitive essays here, culminating in absolute conclusions based on irrefutable evidence. I’m not that smart, nor do I have that much time. I spend my days writing heavily scrutinized material – this blog is supposed to be fun. I know fun and intellectual discourse are not (and maybe should not) be mutually exclusive. However, this blog happens because I have and/or come across an idea or a thought or an amusing/interesting story and I toss it out there. I like to leave the idea open to invite thoughts and comments from others. Laying down dense, erudite material that cannot be argued with is not my style. I invite you to visit both of Milan’s blogs for a more academic conversation. I appreciate how deeply you care about every topic and how much time, effort and research you put into your blog and into all your comments here. It’s astonishing and a little frightening. When I was at university, I could have sat with you for hours in heated debate about philosophy and literature, but these days I’m afraid I just don’t read that much learned material. Day-to-day life and work seem to suck up most of my time and energy. So, I will freely admit that unless it’s a topic I care a great deal about, much of my research will be sloppy and my thoughts only half-formed and expressed. I hope you will continue to challenge and enlighten me, even if the blog is not always worthy of the passion with which you do so.

  21. XUP: Jesus girl, now you’re making me feel guilty. Don’t worry; I do this to everyone, though I never mean any harm by it.

    I should say as well, if it matters:

    “It’s apparently almost impossible to get rational, selfish beings to cooperate for their common good.”

    I said this is dead wrong, but it depends. If you mean the kind of rational, selfish people postulated in the experiment, then yeah, it’s true. It’s only wrong if you extend the statement to encompass real people, who are to varying degrees rational and selfish, yeah, but they are other things also. Thought that warranted clarification.

    When I was a kid my mother used to call me ‘computer-brain’. She is not like me at all; she’s only just barely literate; it’s like she was impregnated by an alien. I talk just like I write, by the way – I go to parties and do alright so long as I can tell when folk’re going blank.

    I’m not so much the pedantic researchy type as the intense truth-seeking type. I appreciate what you say about leaving the discussion open for people; this is why you get a lot more comments than I do, but hey… 🙂

  22. XUP, I love your blog and marvel at the variety of topics you come up with — consistently. Since I clicked over from Exit78 that day, I’ve never looked back. This is one of the few blogs that I make a point of reading, even when I’m busy.

    G, I’m new to your blog and haven’t commented too much… yet. But, I like it over there too; I admire your conviction. Just left you a comment.

  23. Yeah man, I second Davina – I feel like interesting stuff pops out quite easily here.

    XUP, what kind of freelance gigs do you get? Is it marketing blurb? I would love some of that action but they don’t advertise it in the paper… Not looking to poach or anything; just curious.

  24. I think for me the issue with the PD is that part of the presupposition is that YOU ARE GUILTY OF A CRIME. A serious one by the penalty. So do you have any reason to trust another criminal?

    If instead you presuppose that you are both being falsely accused and know that is coming…I think it would be easier to trust someone I felt was a genuinely honest and upfront person with integrity. Trusting another person to hold fast to the truth seems easier and more rational than expecting them to hold fast to a lie.

  25. G – That was not intended to make you feel guilty. I dated a guy like you for several years in my youth. He was 10 years older. All the people he associated with were thrilled because he was now mostly occupied with me at parties, and other social gatherings, so they would be less likely to be cornered by him and treated to a long lecture on the latest tidbit that was fascinating him. I learned a lot from that guy – most importantly I learned that I was smart enough to go to university. Until him, I figured I was destined for a life of sporadic, low-paying jobs. And to answer your other question, I don’t do freelance anymore. I have a full-time gig with the federal government.

    Davina – Golly. Thanks so much. Now I feel all pressured to live up to your praise! Ha ha

    Mudmama – You can take the whole criminal stuff out of it and think of a similar situation in every day life. But yes, you would be much more likely to cooperate with people you know well and trust. It would be interesting to try something similar with a pair of siblings – old enough to reason things out, but not too old — to see what they would do.

  26. that is some serious mind screwing around with stuff. i would stay silent hoping for the best i think. maybe if i didn’t have kids.

    wait, i wouldn’t hang out with anyone that would be bad and go to jail in the first place. or, i hope i wouldn’t.

    i know, easy way out i chose.