Talk:Prisoner's dilemma

From Wikipedia, the free encyclopedia

You have new messages (last change).
Featured article star Prisoner's dilemma is a featured article; it (or a previous version of it) has been identified as one of the best articles produced by the Wikipedia community. If you can update or improve it, please do.
Main Page trophy

This article appeared on Wikipedia's Main Page as Today's featured article on March 16, 2004.
News This page has been cited as a source by a media organization. See the 2004 press source article for details.

The citation is in: "New Tack Wins Prisoner's Dilemma", Wired Magazine, October 13, 2004.

Other languages WikiProject Echo has identified Prisoner's dilemma as a foreign language featured article. You may be able to improve this article with information from the Spanish language Wikipedia.

This article is part of WikiProject Game theory, an attempt to improve, grow, and standardize Wikipedia's articles related to Game theory. We need your help!

Join in | Fix a red link | Add content | Weigh in
Featured article FA This article has been rated as FA-Class on the assessment scale.
Top This article is on a subject of top-importance within game theory.
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics.
Mathematics grading: Featured article FA Class Mid Importance  Field: Foundations, logic, and set theory
Maintained The following users are actively contributing to this topic and may be able to help with questions about verification and sources:
Loom91 (talk • contribs • email)

Contents

[edit] Error in cigarette advertising example?

In the cigarette advertising example the article says: As the best strategy is dependent of what the other firm chooses there is no dominant strategy and this is not a prisoner's dilemma. The outcome is though similar in that both firms would be better off were they to advertise less than in the equilibrium. I don't see how this differentiates it from the standard prisoner's dilemma. In the standard prisoner's dilemma the optimal situation to both players is that they both cooperate so clearly, if you know the other one is cooperating of course you should cooperate too and defect otherwise. Clearly there isn't a dominant strategy. Thus, the optimal strategy does depend on what the other player chooses just as the article says for the cigarette example. Note that I don't like this way of expressing it in either case because the purpose of the strategy is to provide a decision faced with the uncertainty about what the other person is doing. If you know what the other player does the game is completely uninteresting.

Sorry - I just noticed that I mis-remembered the prisoners dilemma. I thought both would go free if both stayed silent (due to lack of evidence or whatever). In that case there wouldn't be a dominant strategy and it would be equivalent to the cigarette example.

[edit] Any 'Usual ranges' of values on the payoff matrix values?

it might be intuitive that the ultimate choice will depend on P (Punishment for mutual defection) in the payoff matrix: for example if both cooperate they will get 6 months each, both get 8~9 years if both defect, and the cooperate one get 10 years if the other one defects (of course the one who defects in this case goes free), then the expectations is the insignificant marginal benefits of actually defecting (just in case the other person/algorithm does defect) that their decision may just as well be cooperating.

From the above, here is an suggestion for a modification to the problem: the rules will be the same except P will have a range, ranging from some attractive values (Close to R) to some severe case (Close to S) so the inequalities T>R>P>S and 2R>T+S are still satisfied, but it's the actual value of P we are hiding from the two prisoners (The range is given and distribution may or may not be available)

Now what is the optimal individual(selfish) decision? does it depend on the fact that the prisoners know the distribution or not?

[edit] learning psychology and game theory

Hello, I wrote that section and nobody has changed it yet. I'm no expert I'm just trying to draw attention to moral dilemmas and developmental psychology. Surely someone else can improve it. It needs references, qualification and perhaps, in part, refutation. Come on if you think your hard enough (joke!).

Andrew Francis


Your article seems a little too much abstract compared to those written by mathematicians or computer experts, Andrew.
Though I'm particulary curious about this topic. I want to assemble bibliography over this, if anybody else... I think of Jacques Lacan's "Le Temps Logique"(in Écrits) which is neglected but important (as so as Hofstadter's example) cross point of computing theories and of psychoanalysis. --NoirNoir 06:28, 16 May 2005 (UTC)

[edit] What is the rational decision?

The article makes a mistake, in that the prisoners do not have to be in contact to reach the mutual best decision. If the prisoners assume that both of them are rational, and bound to make the best rational decision, they will choose to cooperate.

  • Actually, the whole point of the problem is "What is the best rational decision?"
And that is to defect, so the original question presents a misunderstanding.
The whole point is that both decisions are equally rational or irrational. The article says the following "This illustrates that if the two had been able to communicate and cooperate, they would have been able to achieve a result better than what each could achieve alone". This needs to be specified more clearly -- the *total* jail time for both prisoners can be reduced to 1 year if both choose to cooperate, but this is not the best result for an individual (purely selfish) prisoner. The best result there is *no* jail time for oneself. Another issue this line implies that if the prisoners had only been able to communicate, they'd choose to cooperate. This is far from sure. Communication in advance in fact does not weaken this dilemma at all. The only thing needed to create this dilemma is the non-communication (by a reliable source) of the other person's actual decision before you make your own. If the other person's decision is known, there *is* a rational choice to make (whatever your aims may be for you and your fellow prisoner). --Martijn faassen 00:07, 15 Mar 2004 (UTC)
Even if the other player's decision is known, the rational (ie selfish) choice is to defect, because the payoff for unilateral defection is higher than the payoff for mutual cooperation, and the payoff for mutual defection is higher than the payoff for unilateral cooperation. Communication does not solve the dilemma. --Michael Rogers 03:19, 4 January 2006 (UTC)

[edit] Misc comments

Shouldn't it be "Prisoners' Dilemma"? There's more than one prisoner, remember. -- Cabalamat 18:15, 27 Aug 2003 (UTC)

But its an individual's decision

i made a change regarding the tv game show example. i realise that some people in the US may subconsciously feel that a television game show is "real life" and not at all an "artificial setting". But i would think that once they think about it they would accept that a TV game show, controlled by some dictatorial media organisation and mega-bucks, with every aspect of the physical and social environment highly controlled, is hardly a very natural setting... Boud 14:43, 17 Dec 2003 (UTC)

Gotta say, I don't think the Assurance Game or Chicken are in any way variants of the Prisoner's Dilemma... Evercat 23:51, 17 Dec 2003 (UTC)

I don't know where to start editing this, but an important paper appeared in Science_(journal) in by Axelrod co-authored with W.D. Hamilton in 1981, and subsequent contests which should be mentioned as this predates the 1984 book by Axelrod.

Thanks for the reference. Dropped it into the list and made the Refs formatting consistent while I was up. Haven't done anything to compare it against article content, though. Dandrake 20:47, Mar 12, 2004 (UTC)

I've always felt that the basic flaw in the Prisoner's Dilemma is that it is so obviously an artificial set up. Would any real police force set free a confessed criminal? In other words it is solely an intellectual excercise and deliberately unrealistic, so it's hard for me to take it seriously even if it does prduce useful insights. Lee M 02:05, 15 Mar 2004 (UTC)

I guess you wouldn't have enjoyed the debate between Bohr and Einstein when they duked it out over quantum indeterminacy using a silly thought experiment in which a photon is released from a box that's weighed before and after. But they found it useful. Seriously, this thought experiment is a bit unrealistic, but it's analogous to a lot of real-life situations. including the tragedy of the commons; so economists who take game theory seriously have to worry about it. Dandrake 02:23, Mar 15, 2004 (UTC)
Well, maybe I'm just too literal-minded (although to look at my list of contributions you might not think so)...Lee M 01:46, 16 Mar 2004 (UTC)
This is actually a common prosecutorial tactic. A person involved at the lowest levels of a crime is offered freedom from prosecution or, more commonly, a greatly reduced punishment, in exchange for testimony against the defendants whom the prosecution really wants to convict. I think that Martha Stewart's stockbroker's assistant was in this category; he participated in the crime, but because of his testimony he won't go to jail. Anyway, if you don't like the witness setup, the PD situation arises elsewhere. For example, several companies selling a competing product might enter a price-fixing agreement. As long as each of them observes the agreement, all of them will profit by charging prices higher than what the market would provide. One "cheater," though, that reduces its price slightly below the agreed-upon floor, will gain market share and thus make even more profits. Of course, other conspirators see this happening and lower their own prices. Eventually the cartel falls apart. Not all cartels fall apart, but when they do, it's a PD situation -- where each decisionmaker pursues his own immediate interests, everyone is worse off than they would be if each had acted based on a sense of the common good or some other approach that differs from the classical interest-maximizing view of rationality. (Of course, because others can see and react to a decision, the cartel example is closer to the iterated version of PD.) JamesMLane 13:17, 18 Mar 2004 (UTC)

I'm not sure that this picture is really appropriate, since the Prisoner's Dilemma really has very little to do with literal prisoners. Perhaps an image of a strategy table for the game would be more appropriate. Adam Conover 05:22, Mar 16, 2004 (UTC)

The Prisoner's dilemma is a totally abstract concept, so you're not going to get a point-on picture. A board game like you suggest is going to be even harder to "get". I decided to opt for a picture that illustrates the two prisoners themselves and I think it's a good fit, personally. →Raul654 05:25, Mar 16, 2004 (UTC)
Actually, the picture you posted was exactly what I was hoping for. I entirely approve. Adam Conover 09:33, Mar 17, 2004 (UTC)

The diagram to the right of the first explanation (right after the Brief Outline heading) does not match the explanation. Lkesteloot 07:15, 16 Mar 2004 (UTC)

Duly fixed. Only took 6 tries. Damn it's late ;) →Raul654 07:25, Mar 16, 2004 (UTC)
Wow, that was fast! Thanks! Lkesteloot 07:36, 16 Mar 2004 (UTC)

Blah!

[edit] re: the paragraph on communication (1)

I feel the following section is misleading at best:

This illustrates that if the two had been able to communicate and cooperate, they would have been able to achieve a result better than what each could achieve alone. There are many situations in the social sciences that have this same property, so understanding these situations and how to resolve them is important. In particular, it demonstrates that there are situations where naïve reasoning in one's own best interest does not always lead to the best result.

Communication is not a prerequisite here. Unless the two prisoners trust each other utterly, communication in advance won't help them get out of the dilemma. This because there is still the maximum payoff -- convince the other to keep their mouth shut while you confess, thus gaining instant freedom.

It also is completely implicit here what 'better' means. It should be made explicit that the total jail time for both prisoners together is least if both choose to stay quiet, but this isn't best for an individual prisoner. This is actually an important part of the dilemma.

This is repeated later on where it claims that 'naïve reasoning in ones own best interest' is to blame for the non-optimal result. This doesn't make sense as there is no reasoning that is actually the wise choice for a selfish individual.

Furthermore, the prisoner's dilemma is applicable far outside the social sciences. It is also very important to evolutionary biology, for instance.

--Martijn faassen 23:03, 16 Mar 2004 (UTC)

  • I think perhaps you don't understand what a prerequisite is. As stated in the paragraph there are two: to communicate, and to cooperate. Markalexander100 02:04, 17 Mar 2004 (UTC)
(To finish a particular debate before it starts: I don't want to discuss my understanding of certain words. Back to the problem.). Communication is not required to make the choice to cooperate with the other prisoner. Communication also doesn't necessarily lead to the choice to cooperate. The description is therefore misleading at best. In addition as I already mentioned, it is left implicit what 'better' means in this context.
With some good will you can definitely interpret the paragraph so that it is strictly spoken correct, but it certainly could communicate its meaning better than it does not.
I think actually the problem starts in the second paragraph of the description of the dilemma, which describes one particular way of reasoning and one particular outcome. This seems to be a particular resolution of the situation, not the part of the dilemma itself. Is this part of the classical description of the dilemma?
I'd propose rewriting the last paragraph of the "dilemma" and the paragraph under it to something as follows:
Let's assume both prisoners are completely selfish and want to minimize their own jail term. As a prisoner you have two options: to cooperate with your accomplice and stay quiet, or to defect and betray your accomplice and confess. The outcome of each choice depends on the choice of your accomplice. If your accomplice chooses to cooperate and stay quiet, the optimal choice for you would be to defect, as this means you get to go free immediately, while your accomplice lingers in jail for 10 years. If your accomplice chooses to defect however your best choice is to defect as well, since then at least you can be spared the full 10 years serving time and have to sit out 5 years, while your accomplice does the same. If however you both decide to cooperate and stay quiet, you would both be able to get out in 6 months.
The naïvely selfish reasoning that it is better for you to defect and confess is flawed; both would end up in jail for 5 years. Even sophisticated selfish reasoning does not get you out of this dilemma however; if you count on your accomplice to cooperate it may be smartest to defect. However, if your accomplice knows this and thus would defect, it would be smartest to cooperate. And so on. This is the core of dilemma.
If reasoned from the perspective of the optimal interest of the group (of two prisoners), the correct outcome would be for both prisoners to cooperate, as this would reduce the total jail time served by the group to one year total. Any other decision would be worse. In a situation with a payoff structure like the prisoner's dilemma individual selfish decisions are not automatically best if viewed from the perspective of the group as a whole.
The particular example of the prisoners may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature which have the same payoff structure. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics and sociology, as well as to the biological sciences such as ethology and evolutionary biology.
What do people think? --Martijn faassen 22:41, 17 Mar 2004 (UTC)

Understanding the wording of the article would be a good first step. Communication is required because it is the basis for cooperation. At the moment, we have two concise, accurate paragraphs; replacing them with four wordy paragraphs would be counterproductive. Markalexander100 01:48, 18 Mar 2004 (UTC)

(I don't want to go into a debate about my understanding of the English language, thanks.). Communication is not required as the basis of cooperation, as I pointed out several times. Cooperation can be iniated just fine without communication in this case. This is true for many instances of the prisoner's dilemma. The iterated dilemma simulations are a good example - the agents just choose to cooperate or defect without advance communication.
I feel the two paragraphs, while arguably accurate if you already know how to interpret them (what does 'best' mean in this context, what is cooperation), do not explain the dilemma well enough. The text also implies that there is a way to 'resolve' the dilemma, while the idea behind the dilemma is that for a selfish individual involved there is no safe strategy. This is the dilemma. The other party can always choose to defect, in which case the right selfish choice is to defect as well.
[cutting in] But the right selfish strategy is always to defect no matter what the other guy does, unless there's some way in which his action is influenced by yours. Evercat
This is a good description of one form of reasoning. If both reason this way however, you'll both be in jail for 5 years. Hardly the right selfish strategy for both of you. Isn't the dilemma wonderful? --Martijn faassen 22:00, 18 Mar 2004 (UTC)
Sensible strategies to resolve the dilemma arise when there is more context, such as in the iterated variety.
I feel more than a brief outline of the dilemma is needed before launching into a long discussion on the iterated variety, as otherwise one risks a reader's misunderstanding of the basic dilemma. --Martijn faassen 09:39, 18 Mar 2004 (UTC)


Communication is completely irrelevant to the Prisoner's Dilemma. One of the fundamental points of the problem is that neither player knows what the other is going to do in advance: it is impossible for them to communicate. Martijn is quite correct, therefore, to say that communication is not a pre-requisite for co-operation; not in the PD problem, anyway.

The first paragraph of the re-written text makes the mistake of assuming that one prisoner has the opportunity to base their choice on a knowledge of what the other one has done. This is a misunderstanding of the PD problem. The two prisoners make their choices simultaneously, in separate cells, with no possibility of communication — so it is incorrect to say "The outcome of each choice depends on the choice of your accomplice." It would be correct, of course, to say that in an Axelrod-type 'Iterated' PD game, a player's choice will be influenced by the other player's previous choice(s). But, obviously, that doesn't apply in a one-off PD such as the 'classical' scenario.

Apart from that flaw, though, the re-written text looks generally like an improvement to me. R Lowry 19:25, 18 Mar 2004 (UTC)

Thanks. I can see where you are coming from about my first paragraph. I think this was not due to a flaw in my understanding but due to a flaw in not being explicit enough in my own writing. The outcome (in amount of jail time) of the choice does depend on the choice of your accomplice, though, which is what I was trying to point out. The choice of course doesn't as you don't know what your accomplice chose/will choose. Simultaniety of decision is not required. As I wrote earlier way up on this page: "The only thing needed to create this dilemma is the non-communication (by a reliable source) of the other person's actual decision before you make your own."
Here's a suggested rewrite of the first paragraph (split into two).
Let's assume both prisoners are completely selfish and want to minimize their own jail term. As a prisoner you have two options: to cooperate with your accomplice and stay quiet, or to defect and betray your accomplice and confess. The outcome of each choice depends on the choice of your accomplice. Unfortunately you don't know the choice of your accomplice; even if you were able to talk you couldn't be sure whether to trust him.
If you expect your accomplice will choose to cooperate and stay quiet, the optimal choice for you would be to defect, as this means you get to go free immediately, while your accomplice lingers in jail for 10 years. If you expect your accomplice will choose to defect, your best choice is to defect as well, since then at least you can be spared the full 10 years serving time and have to sit out 5 years, while your accomplice does the same. If however you both decide to cooperate and stay quiet, you would both be able to get out in 6 months.
Further tuning is likely necessary. It's clear our communication about this is easy to misunderstand, which shows we should describe things carefully. --Martijn faassen 22:00, 18 Mar 2004 (UTC)
Yes. You're quite right, of course, to say "The outcome (in amount of jail time) of the choice does depend on the choice of your accomplice. [...] The choice of course doesn't as you don't know what your accomplice chose/will choose." I think I just misread what you were saying earlier (although, in my defence, the text did seem to indicate prior knowledge of the other prisoner's behaviour). All in all, I like the new improvements. R Lowry 07:39, 19 Mar 2004 (UTC)


Iteration involves communication- you know what the other one did last time. That's why it's a way out of the dilemma. Markalexander100 01:40, 19 Mar 2004 (UTC)


[edit] re: the paragraph on communication (2)

A question... Where does this:

This illustrates that if the two had been able to communicate and cooperate, they would have been able to achieve a result better than what each could achieve alone.

come from? If you allowed the two prisoners to communicate, and they did so, and went back to their seperate rooms to report to the police officers, how would their situation have been changed from before? Neither has gained any information, as the other's statements made during the conversation have no binding importance. The same argument of "no matter what the other guy does, I'm better of defecting (confessing)" still applies, doesn't it? Either confessing is the right thing to do beforehand and afterhand, or it's neither, right? This has been sort of hinted at somewhere above, but I just wanted to phrase my concern in a consolidated sort of way -- kine

The point is not that communication solves the dilemma; it's that communication allows (but not requires) cooperation, which solves the dilemma. Markalexander100 04:36, 20 Mar 2004 (UTC)

Or, more precisely yet, communication facilitates cooperation, which solves the dilemma. Even with communication, kine is right that one prisoner has the ability to betray the other. Conversely, they can cooperate without communicating. For example, they might have agreed in advance what to do in this situation, or each of them might feel enough loyalty to the other (or to their joint criminal enterprise) to act cooperatively without communicating. JamesMLane 05:44, 20 Mar 2004 (UTC)
"they might have agreed in advance what to do in this situation" which would presumably require communication. Certainly if they're motivated by loyalty, then there is no dilemma, but that's why the statement of the dilemma supposes that they're selfish. Markalexander100 06:06, 20 Mar 2004 (UTC)
As I have argued elsewhere on this page, the issue of communication simply isn't relevant to the Prisoner's Dilemma. The way the problem is set up is that the two prisoners have to make their decision independently, without negotiation or any other sort of communication with each other. That absence of communication is one of the defining characteristics of the PD: neither prisoner knows what the other is going to do, so they each have to make their decision alone, second-guessing the other.
The paragraph that is causing this misunderstanding (the last para in the 'Brief Outline' section), was identified as problematic a few days ago and some possible alternatives were presented (please see above, re: the paragraph on communication). It would be helpful if people could have a look at those and comment on how they could be improved upon. R Lowry 10:25, 20 Mar 2004 (UTC)
"the issue of communication simply isn't relevant to the Prisoner's Dilemma"
"absence of communication is one of the defining characteristics of the PD"
Those two statements are directly contradictory. Markalexander100 02:25, 21 Mar 2004 (UTC)


Well, maybe I chose my words loosely, but hopefully the point that I was making is clear enough: neither prisoner can communicate with the other, so they each have to make their decision alone, second-guessing the other. It is, therefore, nonsensical to speculate about what might have happened if the two prisoners "had been able to communicate and cooperate" - the PD problem simply doesn't allow for that to happen. R Lowry 23:56, 21 Mar 2004 (UTC)
I'm of the opinion that even if the prisoners are able to communicate, the dilemma would still stand if minimizing jail time is the only thing that matters to the prisoners. In reality the situation is messier, and in communication one prisoner could threaten to have his friends kill the accomplice's family if he even thinks of confessing, or alternately promise golden mountains if only the accomplice stays quiet, so non-communication is better to make them into 'ideal selfish agents'. Even non-communication could lead to such speculation though: if you're some unimportant flunky and you know your accomplice is the kingpin of crime, for instance. Anyway, these are all different ways in which the real life payoff matrix is never identical to the pure jail term payoff matrix; these considerations change the payoff matrix.
The real life payoff matrix will be identical to the jail term only if the only thing that matters to the prisoners is minimizing jail time. Communication then cannot help in resolving the dilemma. I'm not sure whether we need to include such a stipulation; the prisoner's dilemma is only an illustration of (and name for) this particular payoff matrix. --Martijn faassen 23:38, 22 Mar 2004 (UTC)


[edit] re: the payoff matrix

The payoff matrix is backwards. According to the article, if you confess involvement in the crime, and your partner denies it, you go free, while he gets 10 years in jail. Clearly should be the other way around.

--Egomaniac 22:34, 17 Mar 2004 (UTC)

I don't think so. The procecutor is trying to get you to confess (about your and accomplice's involvement). The procecutor presumably wants to maximize the amount of jail time spent. Anything is better than both prisoners staying quiet and the crime going unsolved.
If you get 5 or 10 years in jail if you confess, then there is no dilemma for a selfish prisoner. Just deny. Either you get off free (your partner gets 10 years) or get just 6 months both. --Martijn faassen
The point is that the important confession is your accusation of your partner, not of your own involvement. That's the only way the dilemma makes sense -- to "deny" is to deny that your partner was involved, and to "confess" is to accuse your partner of being involved. Otherwise, how can the payoff matrix possibly make sense? --Egomaniac 18:15, 18 Mar 2004 (UTC)
That is a good point. I think I've seen the dilemma described in this way before (googling; yeah, found a description along those lines). So, you and he accuse each other, 5 years in jail for both. Only you accuse the other, you get off, 10 years in jail for him. You both stay quiet, both stay in jail on a minor charge for 6 months. This means that the first paragraph of the 'brief description' could be improved as well. I've been too focused the payout matrix; this is correct. For the theory it's fairly irrelevant how this matrix is motivated in particular but obviously we need to give a good description of it nonetheless. --Martijn faassen 22:00, 18 Mar 2004 (UTC)


I'm pretty sure that the payoff matrix is correct as it stands, in the context of the 'classical' example (ie, the one with the prisoners). The reduced sentence for confession is the prisoner's reward for being a 'grass'. (One concern: I don't think the payoff matrix should have the prisoner get off with no sentence at all when the other denies - I think it should just be a reduced sentence - but that's a relatively small detail.)

I do think, though, that actually the 'classical' example is a little confusing; I made the same mistake as Egomaniac when reading this article, and that misreading is not unusual in my experience for someone trying to understand the classical PD. It's actually far clearer, in my view, to express the PD - as Robert Axelrod, for example, does - in the form of a simple two-player game. When described in that way, the PD payoff matrix typically reads something like this:

Cooperate Defect
Cooperate 3, 3 0, 5
Defect 5, 0 1, 1

I certainly don't think that we should get rid of the classical scenario, because it is very much a part of the PD literature and should stay in the article. But I do think that the other, more straightforward, matrix ought also to be worked into the article somehow — possibly in the 'Iterated PD' section, along with the description of Axelrod's tournament. R Lowry 19:40, 25 Mar 2004 (UTC)

Just a note that I agree with User: R Lowry on working this matrix into the article somehow. Martijn faassen 21:01, 29 Mar 2004 (UTC)

@Cyrius (rv - new version is less clear than old version)

reverted version about paradox in prisoner's dilemma

It can not be "less clear", it makes a different point. The prisoner's dilemma is not primarily about selfish behaviour vs. cooperative behaviour, but leads to a paradox. Even if I don't care about the fate of my fellow prisoner, there are two completely logical rationales with contradicting outcome to what I should do. --Moon light shadow 21:28, 19 Mar 2004 (UTC)

No there aren't - there's only one logical course of action if one is selfish. The paradox is that both persons acting selfishly come off worse than if they'd both helped the other. Evercat 21:54, 19 Mar 2004 (UTC)
Thank you for making my point, Evercat. Having two choices is not a paradox. To restate: the problem is that a prisoner, selfishly trying to reduce his sentence, will increase it. And if you think the prisoner's dilemma isn't about selfish vs cooperative behavior, then I suggest you read the rest of the article. -- Cyrius 22:40, Mar 19, 2004 (UTC)
"a prisoner, selfishly trying to reduce his sentence, will increase it" - not exactly - by acting selfishly, he's always reducing his sentence compared to what he would have got. It's the action of the 2 people together that causes the problem... Evercat 23:35, 19 Mar 2004 (UTC)
Yes, there are. The argument for denying is just as selfish as the one for confessing. The argument for denying is that the situation is symmetrical, and because of that both will take the same choice, if there is a rational choice for the problem at all. You don't need to argue with being unhappy with the outcome of the other argument for confessing here. You also don't need to talk in terms of "cooperation" or "communication" to come to that conclusion.
Having two choices is not the paradox. The paradox that there are completely logical arguments for both choices and both being completely selfish.
I don't say that the dilemma can not be seen as a conflict between selfish vs cooperative behavior, but this is completely irrelevant for the paradox. --Moon light shadow 10:07, 20 Mar 2004 (UTC)
There is no valid selfish argument for denying, as it's easily shown that, no matter what the other guy does, you're better off confessing. The only (selfish) reason for denying is if one believes one's own action will somehow influence the other guy's. Evercat 12:20, 20 Mar 2004 (UTC)
Your common sence leads you on the wrong track, when thinking about a paradox. You can indeed proof that you are better off confessing, no matter what the other guy does. Now forget that for a moment! Forget that you may what them to cooperate! Forget that you labeled confessing as selfish and denying as cooperative! Then, please, read my paragraph again: "An other rationale reasoning goes like this: I know that the other prisoner is in the same situation as I am. If we both decide rationally, we will come to the same conclusion. So we will either both confess and serve 5 years, or we will both deny and serve 6 months. Accourding to this argument it is better for me to deny." --Moon light shadow 13:04, 20 Mar 2004 (UTC)
But this argument is clearly fallacious, since we've already proven that it's always best to confess. I think the fallacy is to confuse what it would be rational for both people to do if they were acting in unison, to what it would be rational for a single individual to do. Although it's true that "if both reason rationally they will reach the same decision", that does not mean that they will achieve the optimal result if they both reason rationally. Indeed, in this case, they get a worse result than if they'd both reasoned irrationally. If there's a paradox here, this is it. But it's just not the case that there are two equally valid ways of reasoning here. Evercat 13:16, 20 Mar 2004 (UTC)
There simply *isn't* a rational path towards minimizing your jail time. Defect or cooperate, both are in a sense rational, it's just that rationality doesn't get you very far. Nor does irrationality. It all depends on the other prisoner. Who has the same problem. This is what makes the prisoner's dilemma such a vexing dilemma. Martijn faassen 20:22, 25 Mar 2004 (UTC)

Is there enough consensus to feed my rewritten paragraphs (in italics above, with 2 amended ones lower down) into the main article? --Martijn faassen 23:38, 22 Mar 2004 (UTC)

Your main concern has been my inability to understand the wording of the text. Since I think I'm at least of reasonable intelligence, I think that is a good argument for the rewrite in itself. Martijn faassen 00:17, 24 Mar 2004 (UTC)
  • I think there is a general consensus that there a problem with the 'communication' paragraph. That has been mentioned now in several separate sections of this Talk page, by different people. Markalexander100 is the only one who has raised any objections to your rewrite, and I notice that they haven't yet tried to rebut my last reply to them (above). I would say you have a majority in your favour. R Lowry 18:48, 23 Mar 2004 (UTC)
Okay, I've gone ahead and landed the rewrite. The next candidate for work is the first paragraph, looking at Egomaniac's concerns there. Martijn faassen 00:17, 24 Mar 2004 (UTC)

At the beginning of the article, I think the table should go _after_ the explanation. Its hard to understand the table without reading the text. Luke 16:33, 29 Mar 2004 (UTC)

Just a note to cheer for User:R Lowry's improvements. Great progress, thanks! Martijn faassen 22:00, 31 Mar 2004 (UTC)

Aw, shucks. :) I'm worrying now that maybe the intro is a bit brief and could do with filling out a little...
Another thing: I've rearranged the order of the classical payoff matrix so that the cooperate / defect sections match the second, 'canonical' one (without actually changing the values - they seem ok to me.) As far as I can see, it was simply a case of changing deny and confess around, but please someone shout if I've got it muddled. R Lowry 20:56, 1 Apr 2004 (UTC)

Some comments about the recent additions to the intro:

Some of the first paragraph in essence repeats some of the preconditions set out in the description of the classic dilemma, though most loosely. I'd also like to see something added about ..but if you choose to cooperate, then the temptation to act selfishly and not cooperate is high..

The key aim, then, of the prisoner's dilemma problem, is to see if cooperation can evolve 'spontaneously' among egoists: that is, to ask if self-interested individuals can come to learn, over time, that their interests are better-served by cooperating with those around them, rather than by solely pursuing their own advantage without concern for others.

I have some difficulties with this text. The prisoner's dilemma itself has no aim. The prisoner's dilemma illustrates a particular situation that by itself is not resolvable in a rational way to either selfish party's satisfaction. I guess the aim of the dilemma could be to illustrate a rather surprising problem: logic doesn't get one out of a seemingly simple situation.

The followup question is that we happen to have all kinds of intuitions nonetheless on how to tackle this. We do feel we can resolve this. It only becomes possible to resolve such situations when either:

  • outside factors come into play which actually adjust the payoff matrix. This is not really the dilemma anymore, though.
  • patterns come into play. Memory, or at the least history (agents may not have an individual memory but their culture or genes may have). The dilemma is played repeatedly (perhaps in different circumstances). Strategies, either rational or evolved, could arise in such a case. Stable conditions can arise where populations of tit-for-tat style cooperators drive out invading defectors. The evolution of morality, etc.

I also don't think the word 'spontaneously' contributes much. A key question is whether strategies can exist or evolve, but they need not be spontaneous at all... Anyway, a bit of a rant. I don't really know what to suggest as an improvement (or I'd done it already), but some further tuning would be a good idea. Martijn faassen 22:49, 7 Apr 2004 (UTC)


My understanding of the introductory text is that is should briefly give a flavour of what the article is about, so repeating in general ('loose') terms some of what follows later on seems to me like a fair way to start the article.
Regarding your comments about the second paragraph, I've tried a small rewrite...
The key problem, then, arising from the prisoner's dilemma, is whether or not cooperation can evolve among egoists: that is, can self-interested individuals come to learn, over time, that their interests are better-served by cooperating with those around them, rather than by solely pursuing their own advantage without concern for others.
R Lowry 09:56, 9 Apr 2004 (UTC)


[edit] Examples

I've added an example of the Prisoner's dilemma I've been pondering on today. It came to me while watching the boring race in the Tour de France today. I'm interested in your comments on this, in my opinion, interesting real-life example of this dilemma. -- Solitude 19:03, 15 Jul 2004 (UTC)

I think you would be interested in the article [Social Science at 190 MPH on NASCAR's Biggest Superspeedways that talks about a similar analysis of 'drafting' in NASCAR racing. Also, and I'm not sure if the previous article uses the term, but these are both examples of Co-opetition where you have to co-operate with competitors to stay ahead of the pack.

I also added that to apply PD in actual police and prosecution procedure is likely to cause miscarage of justice. In u.k. and many other countries, it is banned procedure. God save U.S of A. FWBOarticle 17:35, 23 Jul 2004 (UTC)

[edit] Water shortage: Bad example

I think the payoff matrix for the water hoarding example does not satisfy the requirement that T > R > P > S. One of these is replaced by an equality. If you cooperate you survive. If you are the hoarder you survive. Also, it is a multi-player game whereas PD is (strictly speaking) a two player game. Paul Beardsell 02:30, 24 Jul 2004 (UTC)

Actually that requirement for the payoff matrix looks wrong to me.
I thought there was an additional constraint:
T > (R+P)/2 < S
i.e. alternately cooperating and defecting doesn't result in you being better off- quite the contrary.

This is not a requirement of the standard Prisoner's Dilemma since it is a one-shot game. It may be applicable to the iterated version, but I've deleted the reference in the article since it was in a section talking specifically about the standard, one-shot version. DavidScotson 14:54, 12 Aug 2004 (UTC)

I agree that water hoarding is a bad example of the PD, as it involves many people taking many conecutive moves, rather than a one-shot decision. It's really an example of the Tragedy of the Commons where everyone tries to take too much because they suffer no ill effects from their own overindulgence, yet because everyone else is in the same situation you end up with squabbling lines of wannabe hoarders facing empty shelves and on average everyone loses despite their actually being more than enough water to go round.

Tragedy of the commons is a related area, but unless their are only two players, it isn't the same thing, quite.
Interestingly, tragedy of the commons didn't occur very much in England for centuries; the commons were under joint ownership, and hence they had more effective governance.

[edit] First sentence incorrect

The first sentence of the current version of the article is:

The prisoner's dilemma is a non-zero-sum game that illustrates a conflict between what seems a rational individual behavior and the benefits of cooperation, in certain situations where short-term gains produce later wrongs.

This is incorrect. It refers to the iterated PD. In the PD there is only one "game" and only one outcome. This mistake is made several times in the article.

Paul Beardsell 02:36, 24 Jul 2004 (UTC)

Re-written. Paul Beardsell 07:01, 26 Jul 2004 (UTC)

The first sentence is still incorrect, it now says "The prisoner's dilemma is an example of a non-zero-sum game where the best individual strategy cannot be decided but where the best solution for both players considered as a group is obvious."

I think the jargon-y reference to 'non-zero-sum game' is inappropriate in the opening sentence, but my main problem is with the second half. The best individual strategy can be decided. Defecting, regardless of your partner-in-crime's decision, will always be the best move for an actor who is rationally self-interested (read "rationally self-interested" in this one-shot game situation as "totally selfish and unconcerned about future repercussions, whether external e.g. revenge or internal e.g. guilt"). In game theory terms defecting is a dominant strategy and so both players will always defect.

Of the three statements made in the sentence, I think two are incidental or tangential to the topic (at least to the summary) and the third, as detailed above is factually incorrect. User:DaveScotson 23.02, 28 Jul 2004 (UTC)

We disagree on the best strategy "in game theory" terms and I suspect we disagree strongly. Furthermore I think your understanding of the problem is wrong or you understand the wrong problem. But it is 20+ years since I studied this formally so I am going to do a little research before I tell you you are wrong again! Paul Beardsell 23:03, 28 Jul 2004 (UTC)

I not sure we disagree strongly, we're perhaps just not communicating clearly. When I say best strategy I mean that the individual cannot improve his outcome by changing his decision (see Nash Equilibrium). It is important to note that the best outcome (as opposed to strategy) for an individual player is to defect when the other player is co-operating, which is also the worst outcome for the other player. This outcome never occurs because co-operating is an irrational strategy and so you never get the chance to betray the other player.

The mutual co-operation outcome is only optimum if you are concerned about the players' combined gain (or overall efficiency), though it is also, from each selfish individual's point of view, a better result than both defecting. User:DaveScotson

The PD is a one shot game and neither prisoner knows the other's decision until afterwards so there is no opportunity to change your decision afterwards. The best strategy is always trivially determinable if you know what the other player will do but trivial things are not interesting from a mathematical perspective and in this game and all other interesting games you do not know what the other player/prisoner will do. If cooperating was provably irrational or provable rational then the game would not be as interesting: There would be no dilemma. I think you have another game in mind - one of Hofstadter's or Martin Gardner's variants for the iterated PD, perhaps. The individual's best strategy in the PD does not admit to mathematical Game Theory analysis. If it did then GT would tell us the optimum strategy! But it does not. You think, however, that cooperating is irrational. Not according to GT which helps us not at all, one way or the other, in the standard, one play PD. Paul Beardsell 14:46, 30 Jul 2004 (UTC)

When I mentioned changing your strategy I meant in the Nash Equilibrium sense, i.e. if you were to initially choose co-operate as a strategy and then, before committing to it, look at your alternative you would see that you are *always* better off defecting, regardless of the actions of the other individual. If, in the same situation, you have already chosen to defect, then switching to co-operating would *always* be the worse decision, again regardless of what the other person does. As I mentioned above, this makes defecting the dominant strategy for both players.

If we were placed in a prisoner's dilemma situation right now (say with a 2 Million dollar 'prize' if we betray a co-operating opponent, 1 Million each if we co-operate, 1/2 million if we both defect and nothing if we are betrayed) what would you do? I would defect, knowing that it didn't matter if you were rational or irrational, whether you truly understood the dilemma or not. It wouldn't even matter if you were going to toss a coin to make the decision as I would *always* be better off defecting than if I co-operated. Now, to my mind that means the PD has been successfully analysed by Game Theory to the point were I have a clear and effective strategy. If you would reach a different conclusion, or even reach the same conclusion for different reasons I'd be interested to hear why.

Not *always*. If you "cooperate" and I happen to "cooperate" (even if I choose to do so by the toss of a coin) we both go home richer than if we had both used your analysis. Paul Beardsell 04:22, 31 Jul 2004 (UTC)

(If it helps matters, I too have studied Game Theory, though only six years ago in my case, as part of my degree in economics. I am therefore 99% certain that there are factual problems with article as it now stands e.g. I believe the Hofstadter example is a valid restatement of the PD. I'm familiarising myself with how the Wikipedia works and checking some other sources to convince myself of that final 1% before editing the article. If you can provide any links to support your case, that Game Theory does not indicate that defection is always the best strategy for an individual in a PD situation then I'd be happy to look at them.) DavidScotson 00:51, 31 Jul 2004 (UTC)

The two prisoners each are subject to the same rules and payoff matrix. Each, using your reasoning and Game Theory, decides to confess. But this is not the optimum decision: Each would be better off if they both deny rather than both confess so Game Theory has failed them. But each realises the other prisoner, being rational, is likely also to have reached the same conclusion so they decide to deny. But then the temptation is to confess to get out today, free. So each decides to confess. Each realises the other will have reached the same conclusion. So each decides to allow the other their own degree of super-rationality and each thereby decides to deny. One of them is likely to then betray and each realises this so each now reverts to confess! This is the non-optimum decision. Paul Beardsell 03:33, 31 Jul 2004 (UTC)

Let's for the time being leave aside the question of whether your new winner's game is equivalent to the PD. Let's return to the standard PD and the payoff matrix in the article. Paul Beardsell 03:52, 31 Jul 2004 (UTC)

That there is a Nash Equilibrium only says that there is an equilibrium. A Nash Equilibrium is not necessarily an optimum solution. And the PD is an example of that. Paul Beardsell 03:59, 31 Jul 2004 (UTC)

[edit] Image caption incorrect

Please explain the image caption:

Incompleteness of available information, such as is suffered by a prisoner, is one of the conditions of a prisoner's dilemma situation.

In what way is there incomplete information. The only unknown factor is whether the other prisoner will cooperate or defect. And that is the game! There is no "incomplete" information. Paul Beardsell 01:42, 25 Jul 2004 (UTC)

I have rewritten the caption. Paul Beardsell 07:01, 26 Jul 2004 (UTC)

[edit] Hofstadter reference

The Hofstadter discussion re the swapping of two closed bags is from an analysis of his of the iterated PD. It is not "Another explanation". I intend to remove or drastically re-write this. Paul Beardsell 07:00, 26 Jul 2004 (UTC)

[edit] Defies Analysis?

There is a thread running through the article about whether the Prisoner's Dilemma is easy to analyse. While the discussion here and many of the prominent Google results for the term shows there is confusion about what the Dilemma is and means, I don't think that confusion is a defining characteristic.

Some quotes from the article:

"What distinguishes the prisoner's dilemma from other games is that the scoring (the "payoff matrix") does not allow for easy analysis."

"Even more difficult is the analysis of the iterated prisoner's dilemma"

"The prisoner's dilemma is the simplest game in Game Theory which defies analysis."

I don't really understand what is meant by 'analysis' here. Its usage suggests either an esoteric technical term which I have never encountered, or a non-native speaker trying to express that the outcome of the PD is counter-intuitive or paradoxical. (I don't really agree that it is either of these things purely because of the narrow way in which the game is defined. However, it might appear to be if you approach it from a common sense point-of-view i.e. try and place yourself in the position of the prisoners and think what you would do.) DavidScotson

By "analysis" I meant mathematical analysis. Maths cannot tell you what the best option is: There is no mathematical solution to the best selfish solution. "Mathematical analysis" is, I suppose, a technical term. Game Theory is a branch of mathematics. In the standard rules (and non-iterated) PD neither prisoner can decide on his own best selfish strategy using "common sense" either unless by "common sense" you mean you make an assumption about the action of the other player. And if you do not understand that then probably the article is at fault. This is why the word "dilemma" is used! Paul Beardsell 23:11, 28 Jul 2004 (UTC)

So I have explained what I meant but that helps nothing if that is not what is understood by the reader. Perhaps we should replace "defies (mathematical) analysis" with "the optimum strategy is not discernible." Paul Beardsell 04:02, 31 Jul 2004 (UTC)

Perhaps I am missing something, but the one-shot PD is perhaps one of the easiest games to analyze. The central point is that 'confess' is a dominant strategy. No matter what the other player chooses to do, I am always better off confessing. Hence, the Nash equilibrium is trivial to derive: both confess. Apologies if I am just being obtuse about your meaning about "defies analysis".67.180.24.204 04:14, 31 Jul 2004 (UTC)

As I have said perhaps my terminology could be bettered: Mathematical analysis where this is the search for a Nash equilibrium is quickly successful. But (according to my understanding) a Nash equilibrium is not always an optimum solution and the PD is an example of that. Am I correct? Paul Beardsell 04:27, 31 Jul 2004 (UTC)

Well, yes the Nash equilibrium payoffs in the PD are lower than possible. But, I'm not sure what you mean by an "optimum strategy" as opposed to the Nash "confess always" strategy. Since confession is dominant, it is always the optimal strategy. The larger point is that difficulty is not what distinguishes the PD from other games. There are plenty of much more difficult and unintuitive games around, such as those with no pure-strategy equilibrium. (Discussion refers to one-shot games.) 67.180.24.204 05:10, 31 Jul 2004 (UTC)

But, as I know you understand, each would be better off if both "deny". Game theory and Nash do not help us get there. I'm being picky but I think you mean "confess" not "confess always" because, as you say, you're discussing the one-shot game. Paul Beardsell 05:41, 31 Jul 2004 (UTC)

By confess "always", I meant that it is the optimal strategy regardless of the other players choice.67.180.24.204 06:43, 31 Jul 2004 (UTC)

If I ever find myself in the PD situation I think I will assume that the other prisoner is very smart, that he is not a sociopath and that he is not obsessed by Nash equilibria: I will "deny" and trust that he will too. I think this is the truly rational solution and that it is also truly acting with the most selfish intent. It is the optimum selfish solution on which both parties could agree. The asymetric options are not agreeable to both parties and so each should selfishly realise that these are therefore not admissible as solutions: Each should recognise that the temptation to betray is what drives each to the sub-optimal solution. (Which happens to be the Nash equilibrium.) This should allow each rational selfish prisoner to reject the possibility of either party "confessing". And I have seen this operate between rogues, even enemies, in my school days. Game theory seems not to allow this conclusion to be reached. Paul Beardsell 05:41, 31 Jul 2004 (UTC)

If you trust that the other person denies, then you should confess. This is essentially tautological. A decision to do something else essentially means that the payoffs are mis-specified. For example, you might achieve some intangible psychic reward from denying when the other guy does. Well, then that ought to be built into the payoff matrix. Or, I might care about the other guy's sentence. Again, the payoff matrix should be adjusted. The specified PD payoff matrix essentially _requires_ that you confess if you know the other guy denies. One can think of the PD Nash solution almost as a theorem or a matter of pure logic. The cooperation you observe in your school days may either be because of opportunities for retaliation (eg a repeated game), or because of the payoff issues I just mentioned. In either case, it is not a true one-shot PD. 67.180.24.204 06:43, 31 Jul 2004 (UTC)

Expanding on the prior point. The payoff matrix in the PD is typically specified by years in jail. This is fine, so long as the players utility is a function only of sentence length -- the typical assumption. If utility contains other elements like altruism, or a taste for cooperation then the payoff matrix really ought to be adjusted from years, to some ordinal utility metric. Otherwise, we may rationally observe 'cooperative' outcomes in what appears to be a PD. But, this would simply be because the elements of the game are not fully specified. 67.180.24.204 06:49, 31 Jul 2004 (UTC)

But what if all I care about is my sentence and the other prisoner is similarly motivated. I know that the other player cannot be expected to deny if he thinks I might confess, that he should realise I am in the same position, that he should realise I realise he realises I realise ... and therefore we will logically be compelled to do the same as the other. Thus I exclude the asymetric outcomes. I choose the option with the lowest sentence and deny as will my fellow prisoner. Paul Beardsell 10:12, 31 Jul 2004 (UTC)


Suppose you know for sure that the other prisoner will deny. Now, look at payoff matrix. Are you better off confessing or denying? You are better off confessing. Yes, you absolutely would like to enter into a binding agreement with the other guy to both deny. But, in this case, you can't enter an enforceable agreement. There is no way to convince the other guy you will deny. And, even if you could, he would still want to confess to lower his sentence. That, of course, is why it is a dilemma.Wolfman 17:18, 31 Jul 2004 (UTC)
As I had hoped to have demonstrated, both prisoners realise that Game Theory does not help them get the most positive outcome. All that GT can offer is the suboptimal both confess outcome. Realising this, each should see that whatever one of them decides to do rationally must also be the decision of the other presumably rational prisoner. Should one choose confess because the other is thought to be going to choose deny means that the other has the same temptation and both will end up confessing. This is an unwanted result so both deny. Paul Beardsell 18:35, 31 Jul 2004 (UTC)

And that is why Game Theory is of no help. Paul Beardsell 18:11, 31 Jul 2004 (UTC)

I think I understand your position now. Essentially you are rejecting game theory as a useful method of analysis for the PD. Please correct me if I am wrong, here. But given this is an encyclopedia, an article on the PD would seem to call for a standard analysis. In my view, this article is not really the place for a critique of game theory. Indeed, the PD is commonly understand as a common and classic application of game theory. If you can find a link to someone who has published your critique, perhaps that would be the way to go. But as for an _original_ critique, this is not the place. If you feel strongly about your analysis, you might consider sending it to the Journal of Games and Economic Behavior for publication.Wolfman 19:41, 31 Jul 2004 (UTC)

You are right - I need to quote a reference. But I assure you my argument is anything but "original research" and is essentially a regurgitation of the Applied Mathematics 101 treatment of the prisoner's dilemma as taught to me in 1980. This is old hat. And it is why this game has "dilemma" in its title and other standard games in Game Theory do not. Paul Beardsell 22:13, 31 Jul 2004 (UTC)

Paul, I would be very interested to read a mathematical account of your analysis which predicts cooperation in a one-period game. This is a completely different solution concept than the Nash-equilibrium economists instinctively rely on. I teach the PD every year for a day in my freshman economics class. And if mathematicians rely on a different solution concept for this game than economists, I really need to get on top of that.Wolfman 22:52, 31 Jul 2004 (UTC)

I have been looking for a reference and I had thought several would be readily available. I remain confident that I haven't made this up! The best example I have found of the single-shot cooperation I have found so far is here where the MAD of the cold war did not happen. But their explanation is not the one I advance - they speculate that each side projected their own leader as mad enough to complete MAD despite the payoff matrix saying otherwise. Still looking. Paul Beardsell 23:58, 31 Jul 2004 (UTC)

The mathematician who invented GT provides the "original critique" that Wolfman requires. "To von Neumann, the Prisoner's Dilemma was a paradox that all but destroyed what he hoped Game Theory would accomplish" [1]. Von Neumann did not consider the PD a classic example of GT but an anomaly. Wolfman says: "Essentially you are rejecting game theory as a useful method of analysis for the PD." Yes, I am. And so did von Neumann. Paul Beardsell 02:14, 11 Aug 2004 (UTC)

I'd rather see a link with a bit more weight behind it to support the claim that the PD "defies analysis" or is not a "useful method of analysis" as that article edges on an anti-'left' (his terminology) rant at times. However, putting that issue of reliability aside, the link you give appears to claim something else anyway. As I read the article it is saying that (JVN says) the PD is a paradox, where the rational choice for the individual leads to a sub-optimal outcome for all, which I'm not sure anyone has questioned. And if you read the article's footnote on Nash it seems to echo most of the changes to the article that I still intend to make at some point. DavidScotson 12:23, 12 Aug 2004 (UTC)

By "defies analysis" I meant that GT does not lead to the optimum solution. If that is not what others mean by that phrase then I will change the phrase to something else but my point will stand. The Nash equilibrium is only that: an equilibrium. That the Nash equilibrium coincides with the optimum solution in many games does *not* mean that technique can be relied upon to determine the optimum solution. Also the NE is being used by you (and others) as a synonym for "rational choice". Unless by "rational" you and others believe (a) there is no dilemma and (b) "rational" is that which agrees with the NE. No, there is a dilemma the analysis of which GT does not help us to the optimum solution, and the NE is not necessarily optimal. Paul Beardsell 12:56, 12 Aug 2004 (UTC)

Are we not just going in circles now? Do you believe that I am wrong in my understanding of the Prisoner's Dilemma (as taught in Game Theory classes around the world) or are you saying that the Wikipedia should have an article about the Prisoner's Dilemma with only disparaging references to Game Theory? DavidScotson 14:42, 12 Aug 2004 (UTC)

I cannot say if your understanding is wrong. Indeed I have not really been keeping track of who has said what. But some of what has been said is wrong. "Disparaging"? Where you got that from I do not know. What is certain is that neither is this article the place to only make favourable references about GT. I am repeating my points above not because the argument is circular but because my points are not being addressed. Paul Beardsell 20:56, 12 Aug 2004 (UTC)

[edit] Overuse of "classic"

This creates a false impression. It is a special example of a non-zero game. Most non-zero games do not have the dilemma at the core of the PD. And, if they do, they are called the PD. Paul Beardsell 22:31, 31 Jul 2004 (UTC)

Also, it's funny you should mention the phrase "classic example". This appears to my eyes to be a linguistic tic that afflicts the Wikipedia and I've been spotting it everywhere recently. It appears nothing is just an example of anything, it is always a classic example of whatever even when, as in this case, it is actually an outlier or anomaly and most definately not a classic example in the sense that it epitomises the entire class of things. More mundanely, there's probably many places where that phrase should be replaced with "famous example" or "commonly used example" or other less superlative and more correct language. DavidScotson 12:32, 12 Aug 2004 (UTC)

Yes good point and I have another: Political bias has nothing to do with maths. Paul Beardsell 12:56, 12 Aug 2004 (UTC)

[edit] The same misunderstanding AGAIN

A new paragraph in the article says:

The above formula, then, ensures that, whatever the precise numbers in each part of the payoff matrix, it is always 'better' for each player to defect regardless of what the other does.

No, that is wrong. Unless by putting "better" in quotes it is understood that it is not necessarily "better". It is better only for those who think that following the Nash equilibrium analysis is apt in the PD. What is being said is that there is NO DILEMMA. That what to do is obvious. No! This GT problem is famous for being something GT does not help resolve. Paul Beardsell 21:06, 12 Aug 2004 (UTC)

I'm not sure why the original author put better in quotes, but it is always better (and yes, Nash is appropriate here too). Let me break it down:

  • If the other player co-operates, I can defect or co-operate and it is better for me if I betray them by defecting
  • If the other player defects, I can defect or co-operate and it is better for me if I betray them by defecting

And by better I mean I 'score' higher in utility or reduced sentence or whatever measure is being used to define success.

Therefore defecting is always the best strategy, regardless of the opponent's choices. That's why it is the dominant strategy and why both players will always defect. It is also the only Nash Equilibrium for this game, because no player can do better by changing their strategy.

I'm repeating myself here but I just want to be clear: if my opponent is going to co-operate then I benefit to the maximum amount by defecting. If you could choose both you and your opponents decisions, this is what you would go with.

The only sense in which always defecting is not 'better' is that if three conditions are met I can do better,

A) I know that both players are going to defect and B) I can, with cast-iron certainty, get my opponent to co-operate and C) I can only do so by giving an unbreakable agreement to co-operate in turn

Achieving A is easy, if you achieve B and C then you have changed the rules sufficiently that it is no longer the Prisoner's Dilemma. (And that is what Game Theory teaches us about Prisoner's Dilemmas in the real world. Change the rules!)

DavidScotson 23:02, 12 Aug 2004 (UTC)

I really do understand all that you say. But I do not agree with it entirely: One of the issues is the use of the word "better". Because, let's be plain, the "better" result you contemplate is that they both confess. Whereas we know that there is a BETTER result: That they both deny! That they feel compelled to confess is perhaps true but it is not "better". Paul Beardsell 13:35, 13 Aug 2004 (UTC)

Rationality doesn't always lead to pareto optimality when costless and enforceable side contracts are not possible.Profundity06 22:44, 28 April 2006 (UTC)

The link that I have recently placed at the end of the article is to a document which does a better(!) job than our article at avoiding undefined wishy-washy terms. You might read that and say to me: "See, that is what I was saying all along!" And I say the same to you. We give a false impression of the Prisoner's Dilemma to game theory neophytes here. Paul Beardsell 13:35, 13 Aug 2004 (UTC)

Would "individually better" satisfy your objection? That's always true, no matter what the other guy does. Wolfman 04:31, 20 Sep 2004 (UTC)

[edit] Is this Correct?

If an iterated PD is going to be iterated exactly N times, for some known constant N, then there is another interesting fact. The Nash equilibrium is to defect every time. That is easily proved by induction. You might as well defect on the last turn, since your opponent will not have a chance to punish you. Therefore, you will both defect on the last turn. Then, you might as well defect on the second-to-last turn, since your opponent will defect on the last no matter what you do. And so on. For cooperation to remain appealing, then, the future must be indeterminate for both players. One solution is to make the total number of turns N random.

This seems a bit fishy - http://en.wikipedia.org/wiki/Unexpected_hanging_paradox

Yes, it is correct. Since the only Nash equilibrium in the last period (N) is to defect, you take that as a given in period (N-1). So, in period (N-1) the only NE is to defect. This feeds back to (N-2) etc.
Now, if the ending point is uncertain, this argument breaks down. In fact, if the game end with a fixed probability r in each period, then this is just like an infinitely repeated game with a somewhat higher discount rate. In that case, the Folk Theorem for repeated games holds: any payoff in the convex hull of payoffs (above the minmax) can be sustained as a NE (as the discount rate, including game ending prob, goes to zero). Essentially, that means that 'both cooperate' converges to a repeated game NE. But, it is crucial that the precise ending date be unknown. Wolfman 04:26, 20 Sep 2004 (UTC)

[edit] Ethics of PD....

Whilst reading an above discussion it occurred to me that it might be useful to have a short section about the pratical aplication of the PD according to the sociatal context: I mean that the PD reffered to would be legal in USA, whilst in the UK would be legal - though it's not necessarily so black and white - and their specific requirements as to what payoffs may be legally used. It may be that a discussion of this sort would not be appropriate but I did wonder whether the discussion should at least refer to the ethics of PD (after all, although PD may seem logical it may, to some extent, be undermined by other factors - such is the case in UK). One minor point - 'friend or foe' the US game show had a corrresponding UK show called 'Trust' (aired on Channel four, but now off air) - it corresponded in the logical structure of PB variation employed within the US format (as opposed to any stylistic correspondance). Though i'm not too sure whether this site is specifically aimed towards a US audience, or more broadly towards an English speaking audience ( - oops, have only just signed up to wikipedia, where has it been all my life?!)

[edit] Mutual high beam

I disagree with the high beam example. "It's better for you to leave your high beam on at all times, but no good if everyone does it." Leaving your high beam on disrupts the ability of on-coming traffic to navigate precisely. The safe navigation of other drivers in your immediate vicinity is advantageous to you as any accident is likely to impact you in a negative manner.

Usually true, however the risk is relatively low on dual carriageway roads with crash barriers in between. And the risk isn't usually *that* bad- all drivers have probably had to suffer this at some time or other.

[edit] who invented it?

I would like to know, who invented the problem? Samohyl Jan 16:45, 12 Mar 2005 (UTC)


I don't think anyone knows for sure. (Someone please correct me if I'm wrong.) Plato has a problem called the paradox of attrition. This is an n-person prisoners Dilemma. A two person prisoners dilemma occurs in Hobbes' Leviathan (see his response to the "Foole" in Chapter 15). This is the most I know. I can add a section, but my knowledge about this is only spotty. Anybody know any more? --Kzollman 21:20, Mar 12, 2005 (UTC)

[edit] On my recent extensive edits(25/05.2005)

I just wanted to say that please do not revert my edits just because I edited a Featured Article. Let's discuss what you think is wrong here and take other peoples opinions. It will make for a better article.

[edit] First Comment Evarh

Hi, folks. My name's Doug, and I just made a Wikipedia account tonight. This is my first comment on the WP.

I just wanted to say that this article on the Prisoner's Dilemma is certainly the most interesting and thought provoking dissertation that I have read in the past three years or so, possibly in my entire life (a humble twenty-three years, but I have noticed a couple of grey hairs these past few months or so). I'd love to congratulate the person who wrote it on her or his accomplishment, but it is undoubtedly a group effort, a fact that serves to further bolster my optimistic view that humanity has the capacity to rise up above our own Dilemma and do good for our fellow Prisoners, so to speak.

This is an inspiring piece of work; indeed, it is the reason that I made an account tonight. Kudos all around.

[edit] the lead

The prisoner's dilemma is a type of non-zero-sum game (game in the sense of Game Theory). In this game, as in many others, it is assumed that each individual player ("prisoner") is trying to maximise his own advantage, without concern for the well-being of the other players.

I think this lead could use some work. The part about what kind of game it is can probably be made clearer.-Grick(talk to me!) 07:30, July 25, 2005 (UTC)

[edit] The prisoners dilemma is flawed because it is incomplete

The prisoner's dilemma is basically flawed because it fails to account for the aftermath. The prisoner who serves long incarceration will get released eventually. He will then go on a mission to avenge the other prisoner's treason by killing him, his wife and children or something even worse. The prisoners know very well how treason will inevitably bring them reprisal and so they remain silent, no matter what mathematicians think. This habit is called the omerta and it works in real life, that's why the mafia is invincible. The scientists are really living in ivory towers else they wouldn't invent such unrealistic "paradoxes". 213.178.109.26 20:37, 11 October 2005 (UTC)

To model these situations, there is the iterated prisoner's dilemma. But note that avenging is often ineffective; sometimes it's just better to leave it, because there are far too many other people that can defect you, so you won't help yourself much by avenging to that one. So even the classical model is usually quite accurate. Samohyl Jan 21:11, 11 October 2005 (UTC)

[edit] This is *not* a good introduction

In the introduction section, it now says the following:

It is not necessary to assume that both prisoners are completely selfish and that their only goal is to minimise their own jail terms. However, the cases where either or both prisoners are sufficiently altruistic that they would cooperate, even knowing that the other prisoner will defect, are quite trivial. On the other hand, assuming that the prisoners are completely selfish, as is often done in non-philosophical developments of this model limits the explanatory power of the model. Namely, it does not allow the assignment of an unobservable category of intention to each model. More intuitively, the model does not fit with some (real) people's claim that they seek consensus partly out of altruism. The simplifying dismissal of these altruistic intentions such as above may be made in a more complex model by supposing that the propensity towards altruism is already considered when the relationships among changes in each agent's utility are stated.

This is in my opinion not a good introduction. It is stating an opinion, hard to read, and if this criticism should stand in this article at all, it should not be in the introduction. I think some people have apparently problem with the basic idea that the "dilemma" in the Prisoner's Dilemma derives from selfish intent by the prisoners to serve a jail term as short as possible. I'll change this section to a more sensible introduction. Martijn Faassen 20:20, 26 October 2005 (UTC)

The dab header is such a let-down. All articles should have sufficient background to make it available to the reader (by explaining a bit of the context) - that is not to say the readers have to be taught game theory, just that it should be clear to the reader without having to have such a dab header. Elle vécut heureuse à jamais (Be eudaimonic!) 11:38, 15 January 2006 (UTC)

[edit] Chicken

Over at Wikipedia:WikiProject Game theory it has been suggested that the Game of chicken be removed from this page. I think this is right. I don't see how Chicken is any more like the Prisoner's dilemma than any other 2x2 game. If there are no objections one of us will remove it and replace it with a breif summary of the Centipede game and the Diner's dilemma both of which are very similar to the Prisoner's dilemma. Sound good? --best, kevin ···Kzollman | Talk··· 17:57, 12 November 2005 (UTC)

[edit] Suckers?

Shouldn't "Suckers Payoff" be "Sucker's Payoff", or (if there is more than one sucker) "Suckers' Payoff"?

[edit] overextensive use of the first and second person

Much of the article could be phrased without use of the first and second person. This makes the article as formal and professional as possible. If this isn't cleaned up soon, I'm afraid I would have to nominate it for FAC removal. Sentences like:

When your opponent defects, on the next move you sometimes cooperate anyway with small probability (around 1%-5%). This allows for occasional recovery from getting trapped in a cycle of defections.

Is too informal and rude to the reader (as an encyclopedia) and is not a standard of a featured article, because second person should never be used in an encylopedia when portraying a hypothetical scenario. If we're aiming for professionalism, we should avoid "forcing" a hypothesis on the reader by using the second person. It doesn't need to be used in that scenario - it could be phrased in either the passive voice or a third person "the player's", rather than "your". Elle vécut heureuse à jamais (Be eudaimonic!) 11:53, 15 January 2006 (UTC)

I've purged all the "you"s from the article, except where necessary. Johnleemk | Talk 11:58, 15 January 2006 (UTC)

[edit] Pictures needed

This could benefit from picuteres and such. Can anybody think of some suitable ones? Even color graphs would be a great boon.--Piotr Konieczny aka Prokonsul Piotrus Talk 20:44, 5 February 2006 (UTC)


Pavlov or Simpleton

Very readable article; objecting to "you" is just prissy.

The article doesn’t mention Pavlov or Simpleton (the same thing I gather). Somewhere I read that it was able to take over if, beforehand, Tit for Tat had cleaned out the nasties. That is, it would displace Tit for Tat. As I recall, Pavlov simply did whatever worked before, this being analogous to our tendency to do this time whatever worked for us last time. - Pepper 150.203.2.85 01:35, 12 February 2006 (UTC)


[edit] Cooperation

The cooperation part of the game that beat tit-for-tat upon recognition is something secret societies do with each other. President Bush's secret society Skull and Bones likely has classic secret society rules that means you do not purposely interfere with each other within the society allowing cooperation in a competitive environment where everyone else creates loser dilemmas by non-cooperation and interference with each other (the secret society prospered with itself and has better opportunities as a result). The key is recognizing society members, and then they played the Prisoners dilemma with a specific goal for the secret society.

[edit] interesting application of game theory and the prisoner's dilemma

i recently read the book Games Prisoners Play: The Tragicomic Worlds of Polish Prison by Marek M. Kaminski. in it, he applies game theory to analyze the actions of polish prisoners. the examples are taken from his experience as a political prisoner. i thought the book was well written, and provides an excellent "real" example of the prisoner's dilemma. i didn't want to tread on the wikipedia article so i thought i'd mention it here.Lunch 07:34, 16 March 2006 (UTC)

[edit] First Example

the first example that is shown has the suckers penalty at more than double the punishment penalty which is incorrect in my view as the overall penalty is suposed to get worse with each betrayal so that it is always worse for the group to betray but always better for the indervidual.

(c,c)=(2,2) (c,b)=(5,0) (b,c)=(0,5) and (b,b)=(4,4)

is a much more classical form of the dilemma.

[edit] no temptation

the section of text reading;

If the game is iterated (played more than once in a row), the mutual cooperation total payment must exceed the temptation total payment, for reasons explained later:

2R > T+S

seems strange. without trying to do original work here, just as a reader, the two following things jump out; A) I have been unable to find where these reasons are explained later (probably me being blind) B) this seems to remove the temptation to defect- if the optimal position for both players is to cooperate, then they will cooperate... this changes the fundimental assumptions from the basic game and thus the viability of tit for tat and changes for other iterative strategies become less about the iterations and more about the (enhanced) rewards for cooperation... that formula says this matrix would be valid;

Cooperate Defect
Cooperate 5, 5 -5, 6
Defect 6, -5 -10, -10

in short, shouldn't it be;

T+S > or = R Darker Dreams 22:51, 21 April 2006 (UTC)

The reason was lost somewhere along the way. I've added it now. As for your other comment, the inequality in no way changes the nash equlibriam in the single game, it has an effect only on the iterated version where it makes the equilibriam tend to the Pareto Optimum. Loom91 13:18, 24 April 2006 (UTC)

[edit] Perfectly Rational

It doesn't seem to me as if a perfectly rational prisoner would choose to defect at all in the first place, assuming his prison-mate were also perfectly rational. Since they are both perfectly rational, and they both have access to the exact same information, they would both end up coming to the same conclusion. And since they are both perfectly rational, each would be aware of that fact. So they both know that the only two real possible outcomes are that they both defect or they both cooperate. They will be much better off by both cooperating than they would be by both defecting, so realizing this, would they not choose to cooperate? It seems that you would only get people defecting when they aren't perfectly rational, or they know their partner isn't perfectly rational. Uniqueuponhim 05:46, 25 April 2006 (UTC)

  • It's easy to run into such logical fallacies when using the subjective intricasies of language. That's why game theory is done in the precise language of Mathematics, and it can be proven that the Nash Equlibriam of this game is (defect,defect) and not (cooperate,cooperate). But you make a good point. Loom91 07:45, 25 April 2006 (UTC)
You say that I've run into a logical fallacy, but you do not indicate where. Logically, what would go through each prisoner's mind is the following: "Whatever conclusion I come to, my counterpart will come to the same conclusion and make the same choice, as we are both perfectly rational. Thus, if I choose to defect, he will necessarily choose the same thing. If I choose to defect, the only possible outcome is that I serve two years. However, if I choose to cooperate, then my counterpart will as well, and thus, the only possible outcome is that I will only serve six months. Serving six months is a better outcome than serving two years, so the rational choice would be to cooperate."
The key to this logic is that both prisoners, if perfectly rational, must arrive at the same conclusion. Since they are both perfectly rational, they will also realize this, and know that there is zero possibility of them choosing differently. They are thus only left with the two possibilities of both cooperating or both defecting. Among these, both cooperating is the best choice and so they will both choose that. The only time this wouldn't hold would be when both prisoners are not perfectly rational. Uniqueuponhim 19:14, 25 April 2006 (UTC)
    • The choices of the two prisoners are technically independent, in the sense that they will both do only what their logic tells them to do and is not influenced by the other prisoner. Now from this perspective the questions of what the other will do and what I'll do are not different, though related. I first evaluate the question of what the other prisoner will do and find that whatever the answer is I'll always be better off by defecting, irrespective of whether he coperates or defects. That is why I defect. Loom91 07:35, 26 April 2006 (UTC)
A key point here is the value (or cost) of the "sucker's payoff", that is, what I get if I cooperate but you defect (and the related value of "temptation", that is, what you get for the same result). In Prisoner's Dilemma this is usually a large negative, much worse than the benefit accrued if we both defect. Given this and, as Loom91 notes, independence of the two players (no discussion, no shared history, no knowledge of the other's decision), the only rational approach is to defect. Essentially, why risk the sucker's payoff against someone you don't know and with whom you haven't agreed a strategy beforehand with? Of course, all this changes if, for example, iterative games are played, or if the payoffs are slanted differently (but then, it's not Prisoner's Dilemma then). Hope this helps, --Plumbago 08:54, 26 April 2006 (UTC)
That still doesn't make any sense. My point is that with two rational prisoners, they will both realize that the other one must always come to the same conclusion as he does. I do understand the logic that you are using that states that either prisoner is always better off defecting no matter what the other prisoner chooses, but that doesn't take into account the fact that the prisoners cannot make two different choices, and that they will both be able to deduce this fact.
Without this deduction, it will happen as you explain it: each prisoner will rationally think out: "If he cooperates, then if I defect, I get no time versus six months if I cooperate, so defecting is better in that case. If he defects then I get two years for defecting and ten for cooperating, so again, defecting is better. Thus I should defect." I understand this.
However, with the deduction, it is altered significantly, by removing two of the possibilities. To reflect that, let's reword your logic a bit, to take the deduction into account: "If the other prisoner defects, then he will only have done so when I have as well. So if I defect, we both receive two years. If the other prisoner cooperates, he will only have done so in the case that I will as well. So if I cooperate, we both receive six months." Basically, because you've removed any possibility of the prisoners choosing differently, the prisoner is essentially deciding between two years if he defects and six months if he cooperates, so he will always choose to cooperate. Uniqueuponhim 14:06, 26 April 2006 (UTC)
It seems like you don't understand what rational means in this context. It's not even true that two rational players must employ symmetric strategies in a symmetric game(see Game of Chicken)Profundity06 19:47, 28 April 2006 (UTC)
This is one of those questions where people just talk past each other; it brings up fundamental philosophical questions relating to free will. See also Newcomb's paradox. --Trovatore 13:49, 26 April 2006 (UTC)
Loom91 writes "they will both do only what their logic tells them to do and is not influenced by the other prisoner" which is not entirely correct, in that players base their actions on expected probabilities that other player will play one or the other strategy. The Prisoner's Dilemma has little of this aspect however, since there is a dominated strategy. No matter what the other player cooses, a prisoner's payoff is always higher if he/she plays Defect. If the other player plays Cooperate, then Defect pays more. If the other player plays Defect, then Defect pays more. Phrased this way, it's hard to see how "Perfectly Rational" players are supposed to choose Cooperate. There are cases (see e.g. subgame perfection) in which the Nash Equilibrium isn't something that really squares away with common sense, but the PD is a poor example of such a thing. Pete.Hurd 14:42, 26 April 2006 (UTC)
Ah, but the problem is, you cannot phrase it that way, because what the other prisoner chooses is wholly dependent upon what you choose. The phrase "If the other player plays Cooperate, then Defect pays more" is irrelevant, because such a situation will never arise. If the other player plays cooperate, it is only because you have both arrived at the conclusion that cooperating is better, and thus, are both playing cooperate. With the knowledge that such a situation will never arise, neither prisoner can expect to possibly get zero years by choosing defect, nor can they expect to serve ten years by choosing to cooperate. The choice boils down to simply: six months for cooperating and two years for defecting.
Perfectly rational individuals will realize that NO MATTER WHAT the other player chooses, they are better off defecting and thus, independent of what the other player does, they defect. This particular game doesn't involve much of strategic interest. It doesn't make much sense to say that two people are rational and they each know that but then go on to contradict the usual understanding of rational in game theory-- an expected utility maximizing agent.Profundity06 19:25, 28 April 2006 (UTC)
There isn't even a Nash equilibrium at Defect,Defect either. The Nash equilibrium exists at a point at which neither prisoner stands to gain anything by changing their choice. However, at Defect,Defect, both prisoners know that if they change to cooperate, then the other prisoner will as well, so one prisoner changing from defect to cooperate doesn't change it from Defect,Defect to Cooperate,Defect, but rather changes it from Defect,Defect to Cooperate,Cooperate. Thus, they have gone from serving two years to serving six months, so they certainly stand to gain by changing their choice, and so no equilibrium can exist at Defect,Defect (as long as both prisoners are perfectly rational, of course). Uniqueuponhim 20:32, 26 April 2006 (UTC)
  • "is irrelevant, because such a situation will never arise" not so, what would happen if you were to do something is very important in deciding what to do.
  • "There isn't even a Nash equilibrium at Defect,Defect either" I think perhaps you've misunderstood what a Nash equilibrium is, or how game theory works.
Pete.Hurd 20:52, 26 April 2006 (UTC)
Using the logic of unique, we can construct the following circular argument. If prisoner A determines that they are both going to play Cooperate, the it will be better for A to play Defect. But once A determines that he is going to play defect, it follows that the other is going to play defect too and it will be better for A to play cooperate as B will also lay cooperate then. To be frank, the issue is not completely clear to me either. I think the question is whether two real-world players who are rational in the real-world sense will play the Nash Equlibriam. Loom91 17:36, 26 April 2006 (UTC)
"it follows that the other is going to play defect too *here* and it will be better for A to play cooperate as B will also lay cooperate then" "here" marks the end of the stuff that is correct. Once B decides to defect, A still gains more by defecting. A discoordination game would have the reaction correspondence implied by the rest of your description. Whether (more often, why not) real-world players play the Nash is a very active field of research, see experimental economics. Pete.Hurd 18:27, 26 April 2006 (UTC)

[edit] Iterated Prisoner's Dilemna

The section on Axelrod's writing is interesting. However, I've been told that empirical research tends to show that even if players start out with cooperative strategies, they quickly(within 50 or so rounds) converge to the defection outcome. I should look into it some more.Profundity06 19:32, 28 April 2006 (UTC)

[edit] Pregnancy? What the...?

Found this line in the section A similar but different game: The pregnancy of this problem is suggested by the fact...

So, uh, I'm wondering if the word pregnancy is at all correct here... ``T. S. Rice 23:06, 25 May 2006 (UTC)

Nothing wrong about it, but the wording is not very clear. Feel free to improve. Loom91 06:35, 26 May 2006 (UTC)


[edit] game theory selfish?

the current version claims game theory assumes selfish behavior. this is not true. players maximise their payoffs, but one player may take pleasure or pain from another's success. Evolutionary game theory, for example assumes payoffs are proportional to genes in common.

For those coming to pd for first time looking at the mechanics of the classic case is surely best way to understand the point.

Hofstader's magical thinking should surely be treated as that. given the game the individual raises their payoff by defecting. really it should be struck out altogether. —The preceding unsigned comment was added by DEDemeza (talk • contribs).

[edit] What is to be done?

This may be a featured article but its wrong in many respects. Start with the first paragraph. It claims that game theory assumes each player has no "...concern for the well-being of the other players". This is patently untrue. If players are concerned for others the payoffs change but the rest of the mechanics stay the same. Suppose that jail terms are as described in the "classic example" but each player is fully altruistic putting as much weight on the other player's utility as on their own. Now for each cell each player's payoff is the sum of the prison terms of them both.It is then straightforward that there are two Nash equilibria; both confess and neither do. The point is that there is no conceptual difficulty in incorporating other regarding preferences and this is standard doctrine.

Second, the reference to a banker is odd. In the "classic" example I suppose you would have to say that the banker is the police, but this seems odd terminology. Or what if you took a tragedy of the commons case. each player decides whether to put one or two sheep on the commons. Where is the banker now?

So the first paragraph should delete claim that game theory assumes self regarding behaviour and the reference to the banker.

Many paragraphs have worse problems than this. I don't really know where to start especially as it will all get deleted. —The preceding unsigned comment was added by DEDemeza (talk • contribs).

Game theory assumes that the payoffs reflect the players interests, and that players have no concern for other players payoffs. "Suppose that jail terms are as described in the "classic example" but each player is fully altruistic putting as much weight on the other player's utility as on their own." well then, that's a totally different game once you change the player's payoffs to be something else, it's not the Prisoner's Dilemma at all anymore. This is not a problem with the article, it's you wanting the game to have different payoffs than it does. "The point is that there is no conceptual difficulty in incorporating other regarding preferences" ummm. sure, one could come up with games that do this, but then what you have is something quite different from the topic of this article. Pete.Hurd 23:02, 22 August 2006 (UTC)
Yeah, I'm not sure what the "Banker" is doing in there... Needs a subtle copyedit tweaking, that's all Pete.Hurd 23:09, 22 August 2006 (UTC)

I agree with what pete hurd says but the previous version claims that game theory cannot handle other regarding preferences. This claim is irrelevant to the PD and wrong so the claim should be deleted.—The preceding unsigned comment was added by DEDemeza (talk • contribs).

Game theory cannot handle preferences which are not made explicit in the player's own payoffs. PS Please sign your comments with four tildes, it makes it easier on everyone else. Pete.Hurd 23:17, 22 August 2006 (UTC)

Again I agree but its not going to be helpful to say this in the PD article. But I am mainly hoping I have mastered the signature routine.DEDemeza 23:28, 22 August 2006 (UTC)

Still on the first para, wouldn't it be better to say that cooperate strictlt dominates rather than betray is strictly dominated. Agreed that with only two strategies one implies the other but more generally the relevant concept is the former.

I would not use both "betray" and "defect" even though it is explained synonoms. Confusing at this point. Both terms relate to a context that is not yet explained. Actually, I( doubt this paragraph will mean much to most readers without the basics of game theory, which will be a high proportion of visitors. Many of the rest will already know it. I would go straight to the "classic" example.

Para two. I strongly feel its inappropriate to have the Hofstadter stuff here. It is not made clear that virtually all game theorists regard this as a fallacy (one displayed in earlier contributions to this discussion). So it will only confuse novices. at the least the fallacy should be exposed. Granted the play is independent and the game one shot, if a player switches from the putative cooperative equilibrium in every possible outcome that player will have a higher payoff. Hofstadter probably wants to think the world is like the ideal of a sixties commune but bending logic ios not the right way to do it. Cooperation does occur in the world but its either in the preferences of because many of the relevant games are repeated.DEDemeza 06:59, 23 August 2006 (UTC)

[edit] Generalized form

I don't understand the following passage;

"If the game is iterated (played more than once in a row), the mutual cooperation total payment must exceed the temptation total payment, because otherwise the iterated game would not have a different Nash Equilibrium (see section on iterated version):

2 R > T + S"

It is well known by the folk theorem that the earlier condition T > R > P > S yields an infinity of equilibria in an infinitely repeated game or one with a random end period. So the iterated PD adds a lot of equilibria even without a change of payoffs. A minor pioint is that it is unclear whether the new condition is intended to replace the previous one (then it allows cases that are not PDs) or be a further requirement.

In fact the section is not really a generalisation at all. it just provides a slightly different context. Generalisations, though not specially interesting ones, would be to many players and many strategies. I suppose you could say there is a generalisation in replacing the numbers in the payoff matrix by symbols, but that is not very interesting and if it is to be done does not require a special section. the terminology for the generic payoffs seems to me terrible. But let's not go into that. The whole section should be deleted.DEDemeza 21:55, 23 August 2006 (UTC)

"The whole section should be deleted" not everything that you don't understand ought to be immediately deleted. Pete.Hurd 22:09, 23 August 2006 (UTC)

I am English. What I really mean is that the revised condition is wrong. If you think it is right explain.(the entry on repeated games is fine and confirms my claim). However, my reason for advocating deletion of the whole section is not that that particular point is wrong but that at best it adds virtually nothing to the previous section.

What has to happen before it is reasonable to delete the section?DEDemeza 22:36, 23 August 2006 (UTC)

I'm afraid I don't understand what you are disagreeing with. As I recall the folk theorem has some requirement for the payoffs to be "feasible" or something like that. In particular that the potential punishment from defecting must be sufficiently harsh so as to warrant cooperation. I don't think anything with T > R > P > S will satisfy that, although I may be wrong. --best, kevin [kzollman][talk] 22:59, 23 August 2006 (UTC)

You are wrong. The folk theorem implies that for any PD, with a sufficiently low discount rate (or high probability of continuation) both players cooperating can be sustained as an equilibrium. So too can lots of other outcomes. You might look at the paper on Aumann on the Nobel Prize site. Though as I say this not the main reason for suggesting deletion of the section.DEDemeza 23:13, 23 August 2006 (UTC)

The idea that any game that follows those inequalities classifies as a PD will be new to most readers. It is not commonly understood, outside of mathematics, that classes of mathematical objects can all share the same interesting properties while being instantiated differently. It seems important to me that we explain that a game need not have: (a) those exact jail terms, (b) have jail terms at all, or (c) even be about prisoners. The section, I think, at least gestures in that direction. I agree that it could probably do to be rewritten. On a stylistic note, you would probably find other editors more open to your suggestions if you refrained from calling their writing "terrible." --best, kevin [kzollman][talk] 00:02, 24 August 2006 (UTC)


In fact the article opens with a fairly general statement of the PD. As I said in an earlier talk, this seems to me to probably be inappropriate for most readers who will not grasp the point. So starting with an example is best. However if having gone through this a reader does not realise that the result does not depend on the particular numbers chosen, this article is surely not for them. My inclination would be to start with the classical example pull together the essential requirements and outline a few other applications. Sorry if I was intemporate. Partly the result of my previous talk where it did not seem to be appreciated I was being critical so I thought I need to be more direct. I did not explain why I thought the terminology for the payoffs should be changed as I was arguing on other grounds that the section should go. But if it stays at some point I will make my case. DEDemeza 08:38, 24 August 2006 (UTC)

I see that Loom91 has reinstated the condition for a repeated PD to have an equilibrium other than mutual defection but added a reference to the "Selfish Gene". I don't have a copy to hand but.. 1) The "Selfish Gene" is a wonderful book but it is not an authority on game theory. For example Dawkins would not at that time have known of subgame perfection and probably still does not. 2) It is an absolutely standard result in game theory that any infinitely repeated PD has a cooperative equilibrium when the interest rate is sufficiently low. See for example on the Nobel Prize site http://nobelprize.org/nobel_prizes/economics/laureates/2005/ecoadv05.pdf starting p13. So no extra condition on the payoffs of the stage game is needed if an IPD is to have a cooperative equilibrium. 3) Even if there is some sense in the condition (which I doubt), in the context of an entry it cannot just be plucked from the air without explanation. I have some professional expertise in game theory though I must admit it would not be correct to call me a game theorist. If though it is a mystery to me why the folk theorem is not applicable or what the rationale is of this condition then I do think there is something wrong in what is intended as an expository piece. Certainly when the section was previously defended on the grounds that some readers seeing a numerical example would not understand that these numbers are not necessary for the conclusions to follow.

Well, I have found it instructive to take part in the editing process but I can see it will be too frustrating to continue. This may appear to be sour grapes, but I do think the article is wrong in many respects and in others is written so as to give a missleading impression. I won't be adding it to the references on my handout. Nice photo though. x x xDEDemeza 14:40, 24 August 2006 (UTC)

I was going to make that my last but just to add this point. The extra condition means that aggregate payoff is highest with both players cooperating rather than one player cooperates and the other defects. It is debatable that maximising aggregate payoff is socially optimal but if that were the case and it is desired that both cooperating is socially optimal then the payoffs must satisfy this condition. However this applies whether or not the game is iterated whereas the Wiki passage says the condition is something to do with iteration.DEDemeza 15:07, 24 August 2006 (UTC)

The reason for imposing this condition was explained with an example in Selfish Gene, I suggest you read the chapter Nice Guys Finish First and see if that changes your proffessional opinion. In any case, you are welcome to add your opposition without deleting the existing referenced statement to the article as long as you provide references yourself. Loom91 09:06, 25 August 2006 (UTC)

I don’t have to read Dawkins to know that what appears in Wiki is wrong. I do have to look at the Selfish Gene to know whether what he says is correct. I now have done so and Dawkins is correct, just a bit silly . He mentions the condition p204 but does not “explain” its role till p211 and then a bit obliquely. The Wiki passage is not at all consistent with what Dawkins says. According to Wiki “If the game is iterated (played more than once in a row), the mutual cooperation total payment must exceed the temptation total payment, because otherwise the iterated game would not have a different Nash Equilibrium (see section on iterated version)” As I pointed out in a previous talk (with reference), it is a basic result of game theory that whether or not the extra condition is imposed, an infinitely repeated PD has an infinity of Nash equilibria and also an infinity DEDemeza 19:52, 25 August 2006 (UTC)of subgame perfect Nash equilibria. So it is not the case that the condition is needed to create a different Nash equilibrium to cooperate cooperate if the game is played repeatedly. Fortunately for him, Dawkins does not claim this. What he observes is that if T+S> 2R then the aggregate payoff from cooperate-defect is higher than cooperate-cooperate. If the game is repeated suppose that cooperate-defect is played every period but the players alternate which defects. Then, ignoring discounting (Dawkins does not mention this), both players are better off than if cooperate-cooperate were played every period. So if you define a PD as a game in which cooperate cooperate is Pareto efficient in a repeated game you need the condition. But it is nothing to do with the condition being needed to change the Nash equilibrium as the Wiki entry claims. Actually, I do not think that it is standard amongst game theorists to define a “true” PD as Dawkins does. None of the definitions found on Google do. Here is a typical one “In game theory, refers to a case in which players select their dominant strategies and achieve an equilibrium in which they are worse off than they would be if they could all agree to select an alternative (non-dominant) strategy” so to satisfy this definition the extra condition is not required. Of course Dawkins is free to adopt whatever definition he wants but an encyclopedia should try to give the standard usage.

In summary, if the condition is to be retained the Wiki passage must be rewritten. It is not required to create new Nash equilibria. But it would be better to drop the condition as it has no real role. The whole section should be dropped. The article requires considerable rewriting.

I have reworded the sentence in the article to conform to the facts agreed upon by everyone. I will get a copy of Dawkins and read it sometime next week so that I can chime in on the matter. I don't mean for this version to be the "final" version or anything, just something that minimizes error for the time being. May I again suggest, DE, that you try to be more respectful of others hard work. If I had written anything that is currently in the article, I would be put off by your general tone. Even if everything in the article is wrong, it is the hard work of a volunteer, who is probably not an academic and not used to receiving such harsh criticism. --best, kevin [kzollman][talk] 00:00, 26 August 2006 (UTC)

The additional condition isn't actually original to Dawkins; for example, Axelrod and Hamilton in 'The evolution of co-operation' (Science 1981, 211, 1390-6) (on which the relevant chapter of The Selfish Gene is largely based) state "The game is defined by T>R>P>S and 2R>T+S" (or a similar form of words - I'm quoting from memory). It therefore seems wrong to credit the suggestion to Dawkins - does anybody know who actually suggested it first? Aretnap 20:29, 13 December 2006 (UTC)

[edit] New real world example added.

I've added another real world example, which is a clearer case of multiple subjects than the Commons example.

"Another instance of multiple players in a PD can be seen in a curved exam in schools. If everyone cooperated and intentionally did as poorly as possible, then everyone would receive the same grade, which would then be curved to 100%. However, if any single person defected, then everyone else's grade would suffer tremendously, at the price of the defector's guaranteeing his own 100% grade. The case is almost always that everyone defects, and only a small portion of the subjects will get the high grade."

[edit] Why is game theory background required to read this?

Currently (Dec 9/06), the article starts with this italicized sentence: "Many points in this article may be difficult to understand without a background in the elementary concepts of game theory." Why? I think that level of complexity should be reserved for a game theory textbook. What's wrong with an article that can educate the layperson? HMAccount 02:29, 9 December 2006 (UTC)

Wikipedia tries to balance between two types of encyclopedias. One, like the Encyclopedia Britannica, is for general audiences. The other is a specialist encyclopedia. We have many articles which could never be realistically read by a wide audience, but are nonetheless useful to specialists (e.g. woodin cardinal). For articles like this one, we try to balance both interests. We hope that at least some of the article is readable by a wide audience, while also including some material for the specialist. I think the article does this well, but if you disagree I would be interested to know it. Is there any part in particular that you found difficult to read or understand, which you would like written more clearly? --best, kevin [kzollman][talk] 20:32, 9 December 2006 (UTC)
Hi, and thank you for responding. I came to this article after a player on the TV show Survivor mentioned the prisoner's dilemma, but that wasn't the first time I've heard the concept referred to. There probably is a general audience for it. I don't mind both audiences being addressed by the article.
I found the hardest part to read is the intro, which is full of technical terms. Some examples: game theory, non-zero-sum, cooperate, defect, dominated, equilibrium, unique equilibrium, Pareto-suboptimal solution, iterated, equilibrium outcome, Nash equilibrium.
In addition, the prisoner's dilemma is said to be a game, but I don't see how it is something people play. Is it best described as a thought experiment? Hope these thoughts are helpful. I do appreciate a lot of work has gone into this page so far. HMAccount 20:37, 10 December 2006 (UTC)
The intro of an article must summarise all the important points of the article, which must include the more technical points. In fact, a summary will necessarily be more readily understood by a specialist than a layman because of the lack of scope to explain things. That is done in the next few sections.
In the intro we must present the main features of Prisoner's Dilemma, which can not be done in a limited space without resorting to standard game theoretic terminology. When writing the intro we can not aim to be completely understood by a general audience without sacrificing information.
As for why it is called a game, game in this context is a highly technical term with a mathematical definition which Prisoner's Dilemma fits. That is why it is called a game. This is another part that can only be understood by someone with a background in basic game theory, hence the header. For a layman, I think the term game does a decent job of capturing the essence of the concept. Note the difference between sports and game. Loom91 09:28, 11 December 2006 (UTC)
Thanks also for your response. I hope my comments don't come across as being unappreciative of how much thought has gone into the article, and I am well aware that the introductory paragraphs have probably had more thought put into them than most! I suppose I really only want to point out that from my perspective, the header tag sets a tone of unfairness to the lay reader that perhaps readers more familiar with the subject matter won't have noticed.
In an effort to be helpful rather than just complaining, I'd like to suggest that the editors on this article add a nontechnical first paragraph to increase the accessibility of the article. Some other articles on technical terms that do this well include infinite monkey theorem , proprioception and signal noise, which last I think shows well how to include both a general and a specific definition.
I'll take a stab at this here; would the regular editors agree with an edit like this? (I think if the first paragraph was accessible, the italicized tag that a knowledge of game theory is required would be unnecessary. Once past the opener I definitely enjoyed the article.)
The prisoner's dilemma is a game first devised by mathematicians Merrill Flood and Melvin Dresher, and given its name by mathematician Albert W. Tucker. In the branch of applied mathematics called game theory, the prisoner's dilemma is one of the classic models used to explain how human beings cooperate or conflict with each other while making decisions. Researchers in economics, biology and sociology also find the prisoner's dilemma set-up useful in thinking about how people will behave.
Unlike other two-person games where there is always one winner and one loser (a zero-sum game, for example chess or tennis) the prisoner's dilemma game offers a third option, where the two players can increase their success by collaboration (a non-zero-sum game). The game hinges on conflict and interaction between individual and collective gain.
In the technical terms of game theory, in the prisoner's dilemma, as in all game theory, the only concern of each individual player ("prisoner") is maximizing his/ her own payoff, without any concern for the other player's payoff. In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. In simpler terms, no matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect.
(rest of intro as it stands) HMAccount 17:44, 8 January 2007 (UTC)
You are basically suggesting that the technical terms used are given a short explanation in the intro itself. The only problem with that is the increase in length. A reader looking for information should be able to tell by consulting the intro whether the article interests him and what the main features of its subject are. Too long an intro defeats this purpose. In your suggested intro, the first paragraph is good. But the second is devoted to explaining what is meant by zero-sum game and non-zero-sum game, a topic that is not directly related to the specific game of Prisoner's Dilemma. The goal is to achieve a balance between information and conciseness. Loom91 08:42, 10 January 2007 (UTC)


[edit] Prisoner's dilemma or Prisoners' Dilemma"

Hi all, I'm not a native speaker of the English language, but shouldn't it be prisoners' dilemma (or prisoners dilemma) instead of prisoner's dilemma? Sinas 09:33, 6 February 2007 (UTC)

While there are two prisoners involved, we are meant to put ourselves in the position of one of the prisoners acting indepedently, and hence it is the dilemma of only one prisoner, hence Prisoner's Dilemma. If we were thinking about how they should act together, then it would be the Prisoners' Dilemma. LukeNukem 10:56, 8 February 2007 (UTC)
It's only from the viewpoint of a single prisoner that the dilemma exists. For the two prisoners as a whole, there's no dilemma, both cooperate is the most profitable outcome no matter what. Loom91 06:23, 9 February 2007 (UTC)

[edit] What does the Closed Bag Exchange talk about?

I think this section needs a rewrite, because i can't see what the point of the last part is, neither in itself nor in relation to the prisoners dilemma. It should either be more clearly explained or removed, i think. Bouke 10:16, 12 March 2007 (UTC)

Waited for 7 days for comments, removing the section again Bouke 08:32, 19 March 2007 (UTC)

I did not write that section, but I do not see your objection to it. What exactly do you consider the problem with it? Some of it was written in an inappropriate lecturing tone, but I added back only the part that had something to say. And since the section was in the article untill this discussion started, please keep it in there untill this discussion ends and a decision is reached. Loom91 08:08, 20 March 2007 (UTC)
IMHO, the last paragraph "In a variation, popular among hackers and programmers, ... collect and exchange information about the bag exchanges themselves?" should be deleted. No sources, poor tone, not clearly related to topic of article. Pete.Hurd 14:53, 20 March 2007 (UTC)
If you don't like the tone, feel free to reword. But I can't see how it is not related to the article. It talks about various factors to be considered in an actual implementation of iterated prisoner's dilemma in a virtual population. That seems related to me. Loom91 08:30, 21 March 2007 (UTC)
Aah, its about an "actual implementation of iterated prisoner's dilemma in a virtual population". I didn't make that out of the original section, and i guess that is the problem with it. In that case, it absolutely needs references. If there are none, it is not important enough to include in this page, and/or original research. I don't know how such things are done, but if no one here can find such references, when is it warranted to remove the section? Or is it customary to let the section stand as it is until anyone can improve it? That may take a very long time if there are no references... Bouke 12:03, 22 March 2007 (UTC)
No hard and fast rule about when to delete. In this case, since there are at least a couple of comments questioning the inclusion, and some time has been given to support/reference, we should consider deleting. At any rate, I support the proposal to delete. For the more general purpose of this article, it seems too specialized (and perhaps should have a separate article targetted at technology applications. That said, the issue of iterated PD games is useful and interesting and should be covered, but perhaps with a more general example.--Gregalton 12:24, 22 March 2007 (UTC)

[edit] Generic payoffs

The T,C,N,P payoff matrix seems to be the win-win, lose much-win much, win much-lose much, lose-lose payoff matrix, which makes the following section which deals with the standard Temptation, Punishment etc payoffs make a whole lot less sense. Any objections if I convert it back? Pete.Hurd 20:34, 24 March 2007 (UTC)

OK I'm out to lunch, it was never in T,C,N,P format, it was always like it is now diff, since 15:06, 22 July 2004. I'd prefer a T,C,N,P payoff table to make the text more sensible, as well, instead, opinions? Pete.Hurd 21:58, 24 March 2007 (UTC)
Umm, what are you talking about? Loom91 13:23, 25 March 2007 (UTC)
Whups, \end{incoherantbabbling}, ok, let me try again (with TRPS instead of TCNP, that'll make more sense). The section Prisoner's dilemma#Generalized form, from the start of the third paragraph to the third last paragraph, speaks of the Temptation, Reward, Punishment Sucker's payoffs. But neither payoff matrix in that section uses these payoffs. IMHO, one of them should be deleted and the other changed to:
Canonical PD payoff matrix
Cooperate Defect
Cooperate R, R S, T
Defect T, S C, C
What do you think? Pete.Hurd 15:01, 25 March 2007 (UTC)
Keep the numerical table, as it provides a concrete example. The win-lose table is pretty much pointless and can be replaced by the table you suggest. Loom91 09:56, 26 March 2007 (UTC)
Retrieved from "http://en.wikipedia.org../../../p/r/i/Talk%7EPrisoner%27s_dilemma_95b7.html"