Talk:Prisoner's dilemma/Archive 4

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The iterated prisoner's dilemma and psychology

Let us consider a game there payoff matrix looks like this:

(Players A and B)	Cooperate	Defect
Cooperate	2, 2	-3, 3
Defect	3, -3	0, 0

Let us suppose that A know that B uses the following mixed strategy:
B defects with probability p,
B cooperates with probability q,
B acts like A last time with probability 1-p-q.
The question is- how should play A.
The answer is following.
If p+q is near 1, i.e. B doesn't use strategy "Tit for Tat" the best way for A is use the dominatn strategy- always defect.
At the opposite case, if A often enought uses strategy "Tit for Tat" the best way is- always cooperate.
Using Monte Karlo method I researched different situation.

B strategy	A strategy	Average scope A and B
"Tit for Tat"(p=q=0)	cooperate (p=0, q=1)	A and B gets 2
"Tit for Tat"(p=q=0)	defect(p=1, q=0)	A and B gets 0
"Tit for Tat" but sometimes defect(p=0.1; q=0)	cooperate	A gets 1.5; B gets 2.1
"Tit for Tat" but sometimes defect(p=0.1; q=0)	defect	Both gets 0
"Tit for Tat" but sometimes defect(p=0.1; q=0)	"Tit for Tat"	Both gets 0
"Tit for Tat" but sometimes defect(p=0.1; q=0)	"Tit for Tat" but sometimes cooperate(p=0; q=0.1)	A gets 0.7; B gets 1
"Tit for Tat" but sometimes defect(p=0.1; q=0)	half "Tit for Tat" half cooperate(p=0; q=0.5)	A gets 1.3; B gets 1.9
"Tit for Tat" but sometimes defect(p=0.1; q=0)	mixed strategy p=0.1, q=0.1	A gets 1.3; B gets 1.9

Conclusion: even if opponent mainly uses "Tit for Tat" the best strategy is always cooperate, even if opponent is slightly agressive.

Let us consider the following problem: B knows that A is intelligent enought and tries to get best result and uses the best strategy for himself. What is the best strategy for B?
I suppose that B should sometimes defect and mainly use "Tit for Tat" so that forse A cooperate. In the case the best way for B to chose p slighnly less 0.4. If p=0.4 for A cooperate or defect doesn't have effect on scope, but if p<critical value for A is better cooperate. If p>critical value it forces A to use strategy "Tit for Tat" and sometimese forgive. It immidiately decreases result of B.

B strategy	A strategy	Average scope A and B
p=0.4	cooperate	A gets 0, B gets 2.4
p=0.4	defect	A gets 0, B gets 0
p=0.35	cooperate	A gets 0.25, B gets 2.35
p=0.35	defect	A gets 0, B gets 0
p=0.45	cooperate	A gets -0.25, B gets 2.45
p=0.45	"Tit for Tat" and sometimese forgive, q=0.2	A gets -0.1, B gets 0.9

If gamers can communicate the psychology involves. Because the best way for B (if A is flexible) is to be firm and open to force A do what he needs. —Preceding unsigned comment added by Aleksey463 (talk • contribs) 10:36, 28 February 2009 (UTC)

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)

I think that the anonymous 213.178.109.26 could also share some of his valuable real life experience to explain why Hilbert's paradox of the Grand Hotel is flawed. --Cokaban (talk) 11:01, 15 December 2007 (UTC)

You have not understood the game which stipulates that both prisoners will defect. There are other problems with the PD but this is not one. 129.12.208.30 (talk) 00:19, 18 December 2008 (UTC)

The intro picture...

...is completely ineffective at illustrating the topic. No doubt it was added because articles cannot become featured unless they have a picture, relevancy be damned, but is this really the best we can manage? Maybe some schematic representation of the win/loss matrix? I remember being impressed when ROT13 became featured and got a picture, which does an excellent job of not being redundant. The picture on this page, sad to say, can't claim the same. I'd go so far as to say it's harming the article more than it's helping, all because the FA gods must be appeased. 82.95.254.249 12:33, 27 April 2007 (UTC)

I think your perhaps mistakenly attributing motives here. (FA does require pictures, as I recall.) Either way, I think the picture is nice. Sure it does little to illustrate the topic, but it adds aesthetic value to the article. I disagree that it's "harming" the article in any way. Can you say why you think that? --best, kevin [kzollman][talk] 17:58, 27 April 2007 (UTC)

Because it's forced. It screams: "Look at me! I'm adding aesthetic value! I'm a meaningless exponent of the human preference for visual stimuli!"

Ahem. In any case, I realize these things are completely subjective, but it just looks inane to me. Would you add a picture of a mall to Economy, with some cheery caption that mentions how economic principles are at work in a mall? Maybe in a children's encyclopedia, but an encyclopedia for adults would try to stay more relevant and less distracting.

A picture of a prisoner, in spite of obvious associative thought, has no relevance to an article on the Prisoner's Dilemma. It's just there so there's a picture to look at. I realize that some people actually like that ("that boring text looks a whole lot more engaging with a picture"), I just happen not to be one of them. 82.95.254.249 20:27, 28 April 2007 (UTC)

Looks like April is the month to find fault with this picture. For what it's worth, I agree with you whole-heartdly. --Badger Drink (talk) 18:59, 3 April 2008 (UTC)

Simulations

This article should include results from simulations of the single-shot dilemma - the question of how most people behave in this game shouldn't be left unanswered. Λυδαcιτγ 01:51, 11 June 2007 (UTC)

Here's one answer. Λυδαcιτγ 02:01, 11 June 2007 (UTC)

Agreed there should be evidence. Simulations are not what is required though. It is a summary of the huge number of PD experiments that have been performed (though not as many single shot as multiple round games). A lot of people play cooperate. My view is that this is because many people do not understand the game (see some of the contributions to Talk) rather than altruism. There has not been a clear experiment on this however. Simulation, as normally understood, cannot tell you how people actually behave. The Tversky book, whilst interesting, is only tangentially relevant. DEDemeza 09:21, 11 June 2007 (UTC)

How do you mean an experiment - a situation involving actual jail terms? I think Tversky's results are pretty significant, even if the dilemma is not as severe. I added a sentence about them to the end of the article. Do you know of any other experiments (or simulations)? Λυδαcιτγ 20:40, 11 June 2007 (UTC)

Sorry, I did follow the Tversky link but the book downloads very slowly and you did not indicate where to look in it. Having now looked elsewhere, I assume that you had in mind the Shafir and Tversky (1992) paper which is indeed highly relevant. I interpret it as support for subjects don’t understand the game explanation though other perspectives are possible. Experiments on the PD have been undertaken ever since the 50’s and by now there are hundreds. My preference for the terminology experiment is that I think the PD has always been seen as a stylised artificial construct and we are not trying to replicate how people actually behave when the DA presents them with the specified choices. These are normally referred to as experiments, but I don’t want to get too hung up on taxonomy. I do think there should be a somewhat extended para on the experimental findings. Personally I am a bit busy at present, not really an expert, and have learnt from experience that dealing with criticism of efforts quite exhausting. Obviously I too get quite worked up when I see something that seems wrong!

By the way, the “Friend or Foe” data has been analysed by John List and this should be mentioned.DEDemeza 11:03, 12 June 2007 (UTC)

I plan to remove the sentence One experiment based on the simple dilemma found that approximately 40% of participants cooperated (i.e., stayed silent). from The classical prisoner's dilemma section. There are two reasons:

1. Even though i would not call the sentence ambiguous, it can easily be misunderstood. Someone may falsely get the impression that in 40% of experiments both players played cooperate, whereas the percent of cooperating pairs in reality should have been closer to 16%, if the percent of cooperating players was 40%. So it would be better to write instead which percent of pairs played cooperate-cooperate, which played cooperate-defect, and which defect-defect. Besides, the nature of the experiment is not mentioned at all.
2. A real-life experiment can hardly be relevant to the classical PD. It would be extremely difficult to assure in an experiment that each player be only interested in his own payoff, and would wish to get it as high as possible (this is an essential condition in PD). If this condition had been satisfied in the experiment, then i believe that much fewer than 40% of players would have failed to determine and use the dominant strategy.

However, it could be appropriate to move this sentence, together with the necessary clarification, to a different section. --Cokaban (talk) 10:53, 20 April 2008 (UTC)

"It would be extremely difficult to assure in an experiment that each player be only interested in his own payoff" this criticism is true of all experimental economics, and ought not to be ignored, but the question of human play in PD games is highly relevant. It's an essential part of the PD literature and belongs in the article. Pete.Hurd (talk) 15:43, 20 April 2008 (UTC)

3-player Zero-sum version of Prisoner's Dilemma

I was reading up on games such as Prisoner's dilemma and zero-sum games and hit upon the text that said, "A non-zero sum game of n players can be turned into a zero-sum game of n+1 players, with the last player representing the global gain or loss of the other n players."

I wanted to know if anyone had an idea to make a zero-sum version. I made one myself, and then tried searching on the Internet, with no success.

Basically, there are 3 players, A, B, and C.

During each "round" of the game, each player pays 4 "chips" into a "pot". Then, players A and B go on playing regular PD.

The payoff matrix looks like this:

(Players A and B)	Cooperate	Defect
Cooperate	7, 7	8, 0
Defect	0, 8	1, 1

C gets whatever is left.

After the round is done, the players rotate roles. The game continues until one player has no more chips.

The net payoff matrix in this case would look something like this:

(Players A, B, and C)	Cooperate	Defect
Cooperate	+3, +3, -6	+4, -4, 0
Defect	-4, +4, 0	-3, -3, +6

I think this version is interesting because it takes into effect another player's payoff, that is, if both players compete, another player benefits while if both cooperate, they bring down the other player. In the classic case, the third player would be the prosecutor. If they both say nothing, the prosecutor loses a lot (say, five million dollars in legal costs, considering the jail sentences being considered). If one confesses and the other says nothing, the prosecutor really does not get affected. If they both confess, the prosecutor gains a lot (say, another five million dollars).

My question is, has anyone already done this? Because I made this to be used as a real game. ZtObOr 03:45, 16 December 2007 (UTC)

(Sorry for not signing...)

Interesting. --Cokaban (talk) 13:51, 25 April 2008 (UTC)

I like the logic, but the real-life analogy is a little weak. Likening it to a third suspect might hold a heavier sway, although even that doesn't provide a solid example. Besseme (talk) 17:57, 6 October 2008 (UTC)

introduction

I recommend the first sentence of the introduction be revised to capture the essence of the game instead of describing it. --VKokielov (talk) 14:57, 3 February 2008 (UTC)

Although the issue is a dilemma for "a prisoner", it only exists if there are "prisoners". Hence should it not be called the "Prisoners' Dilemma" rather than the "Prisoner's Dilemma" ? (As well as cheering up Lynn Truss ...)

Less-than-ideal photo

The photo for the current revision of this article reminds me of a really bad textbook. The film noir lighting, epecially in context with the (entirely correct, mind you) title of the article, suggests a stark realism of some sort (for example, Stockholm syndrome), rather than the more-abstract logical puzzle / game theory it is. Something hand-drawn would be much more in keeping with the nature of the article. I would suggest a hand-drawn, simple-outline scene that features both parties, with the central dilemma somehow encapsulated (perhaps via thought-bubbles - it'd be moving from "really bad textbook" to "somewhat simplistic textbook", granted, but still an upward-movement). My skills in the visual-arts are absolutely abhorrent, so any attempt to create the replacement image myself would constitute vandalism - trust me. --Badger Drink (talk) 18:49, 3 April 2008 (UTC)

I agree. Even if you draw a replacement yourself, i will probably not consider it vandalism. How about just a barred jail window in a brick wall? Maybe with four hands sticking out? --Cokaban (talk) 15:24, 10 May 2008 (UTC)

Introduction definition?

The example in the introduction seems to be wrong (there is not motivation for the players at all not to defect), and incomplete (the default prison term seems to be 14 months, which is only alluded to in the subsequent paragraph). Can someone with more insight clarify...? -- Syzygy (talk) 12:24, 21 April 2008 (UTC)

Which example? Which sentence says that there is a motivation for the players not to defect? In the third paragraph, the implied default prison term is 13 months (what they get if stay silent). In the formulation of the dilemma (second paragraph), the default prison term is not essential. --Cokaban (talk) 20:57, 22 April 2008 (UTC)

This is true that there is no dilemma in the prisoners dilemma, as both players have dominant strategies. This has already been mentioned by someone on this talk page. --Cokaban (talk) 21:20, 22 April 2008 (UTC)

Sorry, it shouldn't have been "example" but "definition". Anyway, the first definition completely fails to mention what happens if both players cooperate (as is explained in the second, "classical PD" definition). If the cooperation (or non-cooperation) between the prisoners doesn't affect the outcome, the whole situation is completely trivial, and I don't think it is what generally is considered a prisoner's dilemma. IMHO the definition currently in the intro should be replaced with the second "classical" definintion. -- Syzygy (talk) 10:40, 23 April 2008 (UTC)

The definition in the Introduction is the "same" as the "classical" one. I do not really see any difference, other than precise jail terms the prisoners are facing, and i do not know why the definition in the Classical PD section should be called classical, as it is not citing any source. Anyway, why the precise numbers, 5 years or 10 years, are important? The definition in the intro does not mention the default term for brevity. The exact default term (say, 13 months) does not affect the dilemma in any way, and can be chosen arbitrarily. (Even the prisoners themselves don't need to know the default term to determine their best choices.) I thought also the definition was rather clear about what happens if the both prisoners co-operate, it is if they both stay silent: they get their default terms. What is the difference that you see between the two definitions? --Cokaban (talk) 11:37, 23 April 2008 (UTC)

On the second thought, i agree that the definition in the introduction is not as explicit about outcomes of prisoners' choices as the one in the Classical PD section. On the other hand, it is 5/4 times shorter, so better for the introduction. Feel free to make it more clear if you can. In fact, i wouldn't mind if the Classical PD section was removed altogether, and the definition from that section replaced the definition in the introduction. Since Classical PD is classical, it should be defined in the introduction, and then it does not need a separate section. --Cokaban (talk) 11:40, 25 April 2008 (UTC)

Hi Cokaban, I tried to improve on the article, though I'm not really an expert on the subject. Now I'm a bit puzzled by the paragraph:

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, all things being equal.

Isn't the point of the PD that if both cooperate, they're better off than if both defected? The paragraph as currently stated implies that defection is always the better option. What am I missing? --Syzygy (talk) 08:53, 28 April 2008 (UTC)

What you say is of course true: if they both co-operate, they both will be better off than if both betray. I do not see anything wrong with the paragraph either: for each of the prisoners, it is always better to betray, as he will receive a shorter sentence, compared to the one he would have received if stayed silent in the same situation (prisoners make their choices independently). Both these statements follow simply from the conditions of the game (or from the payoff table, if you wish). What is the contradiction that you see? By the way, before you find the answers to your own questions about PD, please be careful when editing the article. --Cokaban (talk) 12:02, 28 April 2008 (UTC)

The contradiction is in the statement "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, all things being equal.". But, it would be a "greater payoff" for them to both stay silent, rather than both defecting. Yet it says that the greater payoff would always come from "defecting" no matter the other prisoners choice. Which is true (I'll come to that later), but I think the way it is worded is a little confusing.

The paragraph: It is always better to defect.

IRL: It would be better to stay silent if the other player does than if they both "defected".

Now, to explain it, it is based on the fact that your decision will not change the other players decision. So, if he stays silent, while it would be more beneficial for you to stay silent than to both defect, it would in fact be more beneficial for you to defect in the case that the other player stays silent than not to. It would also be more beneficial for you to defect if he defects than for you to stay silent.

I hope I've explained it satisfactorily.--Person012345 (talk) 09:39, 18 July 2008 (UTC)

Batman Movie Not On Target

Deleted "Media Examples" and reference to July 2008 "The Dark Knight". Not all dilemmas qualify as "Prisoners' Dilemma", and the scenario in the movie misses on at least one of Axelrod's identified criteria, namely that the "reward" for cooperation be greater than the "punishment" for mutual defection.Phaedral (talk) 21:26, 23 July 2008 (UTC)

But the reward for cooperation was greater than the punishment for mutual defection: By cooperating, the two boats would survive longer with a clear conscience while waiting to be blown up by the Joker. By mutual defection, they both would have died quicker, felt worse about doing it, and saved the Joker the work. At least that's how I saw it. I'm not saying that it should be added back in, though. Cooljeanius (talk) (contribs) 05:40, 1 December 2008 (UTC)

But they can't have mutually defected. Once one defected, the other would have been unable to (by virtue of being dead). On a somewhat unrelated side note, it's pretty clear from his behavior in the rest of the movie that the Joker lied about the triggers controlling the bombs in the other boat. - Richfife (talk) 18:01, 10 February 2009 (UTC)

I agree that mutual defection was considered intentionally impossible (or at least highly unlikely). Furthermore, it seems pretty clear that the rules were stated falsely by the Joker; at the least, it seems the boats' detonators would have triggered their own bombs, not the others'. Worse yet, the execution failed, and Batman managed to thwart the Joker, making mutual cooperation the best outcome for both boats. And I'm just getting started. Mutual defection is hardly worse than mutual cooperation; rather the two differ insignificantly by just a few minutes maximum. And the question was clearly above all one of morality, a subject which the prisoner's dilemma carefully avoids. The situation is ridiculous if stated from a purely self-interested standpoint. Finally, the section is superfluous given that there exist many other examples in that section, and it is poorly written.

FOR THE ABOVE REASONS I have removed it again from the article. Eebster the Great (talk) 08:03, 2 March 2009 (UTC)

Cartel members

Members of a cartel are also involved in a (multi-player) prisonners' dilemma. This statement from the article seems dubious since cartel members communicate: A cartel is a formal (explicit) agreement among firms. Please use a cite note to show where this comes from, otherwise I propose deleting this on grounds of original research. — Daniel Mahu · talk · 07:38, 20 October 2008 (UTC)

It's extremely common as a model for cartels or potential cartels, or whatever. The devil's in the details, then, whether they can arrange things to continue cooperating. I added one ref. CRETOG8(t/c) 09:53, 20 October 2008 (UTC)

Surely this is wrong?

From introduction:

"In simpler terms, no matter what the other player does, one player will always gain a greater payoff by playing defect."

and

"Since in any situation playing defect is more beneficial than cooperating..." —Preceding unsigned comment added by 61.19.65.78 (talk) 21:45, 7 November 2008 (UTC)

Nope, those are both correct for the basic definition of Prisoner's Dilemma. It gets potentially different in repeated games, or with different attitudes, or... But in the basic game, defect is the dominant strategy, which means just what you quote above. CRETOG8(t/c) 21:48, 7 November 2008 (UTC)

I must be misunderstanding something. As you know, in the case where both players cooperate you have a situation in which the player is better off than if they had both defected. This seems at odds with the two sentences concerned. —Preceding unsigned comment added by 61.19.65.112 (talk) 15:18, 8 November 2008 (UTC)

The idea is that if the both cooperate, that's better for each than if both defect, as you say. BUT, if the other cooperates, I'm better off defecting; and if the other defects, I'm better off defecting. I think that's clear in the first sentence above, maybe not in the second. If you can think of better phrasing... CRETOG8(t/c) 15:36, 8 November 2008 (UTC)

You say that "if the other cooperates, I'm better off defecting; and if the other defects, I'm better off defecting." But the first part ("if the other cooperates, I'm better off defecting") contradicts the sentence before it. If the other player is cooperating, you will be better of cooperating (6 months in prison) than defecting (5 years in prison). What is it that I'm not getting? 79.138.195.136 (talk) 03:28, 6 February 2009 (UTC)

No, if the other player's cooperating then you're better off defecting (go free) than cooperating (6 months). This is what makes this situation interesting and nontrivial.radek (talk) 03:35, 6 February 2009 (UTC)

Yeah, you're misunderstanding the table. If A cooperates while B defects, B goes free while A serves five years. It's true that the TOTAL time spent in prison is greater than if both cooperated, but the problem assumes that each prisoner acts in total self-interest, so they don't care how long the other spends. Eebster the Great (talk) 04:34, 7 February 2009 (UTC)

It's right alright, defecting is a dominant strategy.Chanology (talk) 19:28, 19 February 2009 (UTC)

Making game theory rationality look better than it is

When people make statements such as "iterated prisoner's dilemma allows for cooperation to evolve", they forget that this is not true when the number of encounters is known in advance. When you are told how many times you are going to play, you should defect every time according to standard economic rationality. It's nonsense, but that's what the theory says.

Axelrod's tournament fixed the number of encounters ahead of time, and all-defect was the dominant strategy in his tournament. All defect was a competitor, and fared worse than any other strategy. The reason people don't mention this is because economic theory is falling flat on its face. But Wikipedia is not censored.Likebox (talk) 05:49, 12 December 2008 (UTC)

Yes, but the number and composition of participants was not known in advance which introduces uncertainty into the situation in a way parallel to a repeated PD with some exogenous probability of the game ending at the end of each round. Axelrod's tournament is a simulation (and is best analyzed with) of an evolutionary game and as such it's not surprising (which doesn't mean trivial) that it is best analyzed with methods from evolutionary game theory rather than the more vanilla version we're dealing with here. So Axelrod's tournament's fine. And PD theory's fine, not nonsense. They're just different set ups. No reason to grind your axes into particles.radek (talk) 14:14, 7 February 2009 (UTC)

Sports Analogy

Not referenced, in any case does not seem to be a particularly helpful example of the PD. In this example, one person will always end up losing, this is not a PD, the incentive structure is different surely?Janamills (talk) 00:23, 18 December 2008 (UTC)

If nobody can defend this analogy in the next week, I will delete it. It reads badly and seems more like a cycling fan praising the sport than a legitimate exercise in economic theory. Who cares, for example, what makes cycling "an exciting sport to watch?" Eebster the Great (talk) 03:23, 30 December 2008 (UTC)

Agree with removal. Most if not all sports situations are zero sum or constant sum games. PD is a negative sum game. Different game. Remove. Also, I still think the Superrationality section needs to go per FRINGE.radek (talk)

Steroid use in sports

Is this a worthy example:

The Prisoner's dilemma applies to the decision whether or not to use performance enhancing drugs in athletics. Given that the drugs have an approximately equal impact on each athlete, it is to all athlete's advantage that no athlete take the drugs (because of the side effects). However, if any one athlete takes the drugs, they will gain an advantage unless all the other athletes do the same. In that case, the advantage of taking the drugs is removed, but the disadvantages (side effects) remain. - Richfife (talk) 20:49, 9 February 2009 (UTC)

ref - Richfife (talk) 21:20, 9 February 2009 (UTC)

Yeah this will work as long as we assume that athletes and fans only care about the relative ranking and that the performance enhancement is not proportional to an athlete's intrinsic ability.radek (talk) 03:33, 10 February 2009 (UTC)

equilibrium coperative/not ?

reading the article, it says at one point: "By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators."

reading it in context, shouldn't it be "...one another in a cooperative equilibrium, relative to non-cooperators." ? otherwise the sentence doesn't quite parse for me.

--Richlv (talk) 18:11, 16 April 2009 (UTC)

I think the idea is that cooperative equilibrium would be both sides cooperating every round, while non-cooperative equilibrium is each side alternating between cooperating and defecting. These are the two equilibriums possible for Tit-for-Tat vs. Tit-for-Tat, and both have ultimately the same payoff. Eebster the Great (talk) 01:39, 17 April 2009 (UTC)

O.K., so I just read the part of the article you quoted, and this is the implication. In a continuous case, strategies like Tit-for-Tat don't work, because one strategy could defect very slightly more often than the other and gain a large advantage as a result. On the other hand, in the discrete case, such a strategy is unsuccessful when facing (for example) a Tit-for-Tat machine, because the user will always be penalized at least as much as any gain he could achieve. Eebster the Great (talk) 01:42, 17 April 2009 (UTC)

Oh, and another potential point of confusion: I think a "non-cooperator" refers to one who either always defects or defects somewhat more often than Tit-for-Tat. Eebster the Great (talk) 01:43, 17 April 2009 (UTC)

The Prisoner's Dilemma does not take into account the benefits of personal integrity for moral agents

Self-interest in this game is depicted entirely in terms of rewards and punishments. Enlightenment, when it is even considered, is presumed to be farsightedness in anticipating rewards and punishments. It is therefore concluded that rationality involves minimizing a narrowly-defined concept of personal punishment and maximizing a narrowly-defined concept of personal gain.

The world view of a moral agent is a part of that agent. Therefore, inconsistencies in that view amount to inconsistencies within the agent, which amounts to a lack of integrity. Integrity is equivalent to being; to the extent that a moral agent lacks integrity it can be manipulated by its environment (e.g., through rewards and punishments, as described in the cited "dilemma") and because it is thus determined by its environment, its being (as a distinct aspect of its environment) is proportionally diminished (i.e., it gets "pushed around" by circumstance, and becomes mere flotsam).

There is no more fundamental interest that a moral agent has than its own being, and so it is in the interest of a moral agent to preserve the integrity of its world view.

For such an agent to pursue its own narrow self-interest at the expense of other persons involves making an unwarranted exception for itself vs. other persons. That is, any argument that could justify such favoritism could apply just as well to any other person besides the agent, and so for the agent to pursue its own interest to the exclusion of that of others involves making an unwarranted exception for itself. Such an exception destroys the integrity of the agent, and so to make such an exception is not in the interest of the agent. This means that the agent would refuse to cooperate with the oppressive authorities (who clearly care nothing for the truth) "on principle." This is related to Kant's categorical imperative: that one should not behave according to a given rule unless one would be willing to have everyone behave according to that rule.

This insight was at the heart of Gandhi's movement of non-violence, which represents a classic and utterly conclusive refutation of any pretensions that the prisoner's dilemma might make of representing some universal rule of human behavior. Thousands of people were killed by the British occupiers in response to Gandhi's nonviolent campaign for Indian self-determination, and yet they persevered despite such personal consequences. Part of Gandhi's method involved individuals and communities being willing to suffer great hardship, including loss of life, because of their understanding of, and commitment to, the larger movement and its objectives. They acted, according to propagators of the prisoner's dilemma, "irrationally," but quite rationally according to the terms I have outlined above. Diversitti (talk) 11:01, 16 June 2009 (UTC)

Hofstadter's Superrationality

"Also, I still think the Superrationality section needs to go per FRINGE." radek (talk)

Is that why the Hofstader section is tagged? As one unfamiliar with this topic, the Superrationality section clarified some confusion I had when I initially read the "rational" argument in the intro. If it is removed perhaps more explanation might be needed in the beginning of the article as to why that choice is considered the "rational" one.

Also, though unfamiliar with the topic, I have have heard of Hofstader (notability). So long as this theory falls within his main body of work, is relevant and addititive to the arguments in the article and isn't being cited as a singular accepted view, why would it be considered fringe? Lacrimulae (talk) 16:44, 18 September 2009 (UTC)

Two proves that defect every time is the dominant strategy for known N

There are two proves for the above fact in the article, once at the beginning of the section "Iterated prisoner's dilemma" and once at the end of that section. The whole second last paragraph of the section just repeats things that where already mentioned above. But I have no idea about game theory so someone else delete it ;) I think this fact is important enough to be at the very top but the second version may be more accessible.

T3kcit (talk) 02:36, 30 April 2009 (UTC)

I agree that the results are redundant and poorly written. I will restructure the iterated section when I have some time. Further, that section mixes classical game theory and evolutionary game theory without really talking about the distinction. -DFRussia (talk) 19:40, 13 November 2009 (UTC)

The write up on this suffers a lot from being based on only the most basic of game theory. "If the game is played exactly N times and both players know this, then it is always game theoretically optimal to defect in all rounds" is simply not true under the stated assumptions. Aside from the assumption about caring only about one's own jail time, it must also be assumed that both of them are rational, and also that both of them know that the other is rational and cares only about his own jail time. If even a small proportion of the population is 'naive' and adopts a trigger strategy (co-operate until defect), then if neither side knows if the other is naive or rational, it will induce a lot of co-operation (as they will have an incentive to pretend to be naive). This will be true even if both of them are, in fact, rational. Similarly, "If the number of steps is known by both players in advance, economic theory says that the two players should defect again and again, no matter how many times the game is played" is also flawed, particularly once you consider that the necessary assumptions to make it true clearly do not hold in practice. 163.1.146.89 (talk) 11:32, 25 November 2009 (UTC)

Sevilla Martínez

An IP editor has been adding (without edit summaries) material apparently from Joel Sevilla Martínez's doctoral thesis. This isn't appropriate. From the point of view of Wikipedia, a thesis is not a reliable source. Often part or all of a thesis is published in an academic journal. If this is the case with Sevilla Martínez's thesis, that publication could be referenced. Although, there has been so much written on the PD that even if it is published, it might qualify as WP:RS but not be significant enough for this article. That would depend on the specifics. CRETOG8(t/c) 16:50, 1 October 2009 (UTC)

If this work has not been cited and used pretty widely, then it fails WP:UNDUE. The PD is a topic of a great deal of scholarship, and this article ought to present elements and aspects of that body of work in proportion to their prominence within that literature. I'll revert once, and would ask that evidence that this thesis work has demonstrable impact be presented if it is to be reinserted. Pete.Hurd (talk) 21:29, 1 October 2009 (UTC)

Closed Bag Exchanges and Street Drug Dealing

The following paragraph in the article:

"even if it is in both their best interests to do so." this sentence´s based on pretending that only external and shortisghted "interests" exist. fact is that internal disprofit occurs it´s also a sign for a wider sight of the situation. in short: when both profit (and still have more than enough to live) a third party might disprofit from the situation without knowing it since this third party´s also short sighted and therefore thinks that her disprofit was her own fault.

87.152.123.202 (talk) 20:23, 16 March 2010 (UTC)

Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.

reminds me of the open-air drug markets in places like San Francisco's Haight-Ashbury district. To somewhat reduce the obviousness of what they are doing, drug sellers and buyers will use "novel" means of exchanging money and goods, like putting one inside a cup which should have soda inside, with a lid on top and a straw sticking out. The other might place the money ( or the drugs ) between pages in a folded newspaper. In this situation, exactly the same amount of trust is required, and indeed the payoff matrix is identical, as described by Hofstadter.

Obviously I have no reliable statistics, however, defection must be rare enough for this practice to remain widespread. To some extent this is due to tourism ( ie the vanishingly small chance of two "players" meeting again in future ), and there are many other factors which can help explain this behavior. However, the close analogy makes this relevant to the article, and, I believe, the taboo nature of this subject lends interest ... while still modeling human economic interaction with a heavy reliance on trust.

I would love to see something about this in the main article, if others agree with the relevance and think this example helps new readers gain insight? —Preceding unsigned comment added by 206.57.60.147 (talk) 23:34, 30 October 2009 (UTC)

Daniel Ashlock in his book Evolutionary Computation for Modeling and Optimization also uses the example of drug dealing.

69.156.179.128 (talk) 05:05, 18 December 2009 (UTC)

Alexrod's Four Rules

I see nothing about non-envious in his four rules. The passage reads:

`` The analysis of the data from these tournaments reveals four properties which tend to make a strategy successful: avoidance of unnecessary con- flict by cooperating as long as the other player does, provocability in the face of an uncalled-for defection by the other, forgiveness after responding to a provocation, and clarity of behavior so that the other player can recognize and adapt to your pattern of action.

The fourth Alexrod rule is `clarity of behavior' —Preceding unsigned comment added by 69.156.179.128 (talk) 05:09, 18 December 2009 (UTC)

"a 'nice' strategy can never score more than the opponent"

This isn't true. Wouldn't a strategy such as "cooperate until opponent defects, then always defect" be "nice" yet still win?

C,C
C,D
D,C
D,C
D,C

24.34.94.195 (talk) 02:34, 31 December 2009 (UTC)

maximizing his or her own payoff

The phrase in para 3: "In this game, as in all game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff" is slightly misleading. It might mean maximising his expectation payoff subject to judgemants about what the other player is likely to do. In the classic von Neumannnn and Morgenstern treatment of zero-sum games (The English translation is called "The Theory of Games and Economic Behaviour" published about 1935)each player seeks to mininimise his maximum loss (equivalently maximise his minimum gain).

78.149.201.243 (talk) 12:44, 20 December 2009 (UTC)

For minimax, von Neumann can do it that way since, being zero-sum, it's equivalent to maximizing own (expected) payoff. But, there are exceptions in game theory, so I switched the "as in all" to "as in most". CRETOG8(t/c) 15:36, 20 December 2009 (UTC)

this analysis is too hidebound, in that the rational prisoner will also look to the political consequences of any act of betrayal both in custody and on the street in terms of his obtaining a reputation as a "snitch" or informer, the consequences of which can become very drastic. Thus what is really in the prisoner's interest must be viewed more broadly: keeping silent and doing 6 months is the most prudent choice; in fact keeping silent would be the best choice in all except the more extreme scenarios as a death sentence from other prisoners and gang members on the street is a likely outcome of informing in many situations. —Preceding unsigned comment added by 173.16.203.56 (talk) 01:09, 31 January 2010 (UTC)

It is usually assumed that there is no way for anybody to ever find out if either prisoner defected; they do so in secret. Either way, it doesn't matter: the dilemma is used as an example, not for a literal scenari.Eebster the Great (talk) 16:35, 31 January 2010 (UTC)

XKCD references are not appropriate

See Wikipedia:XKCD. Please stop adding them to the article, and future articles. Snied (talk) 06:35, 1 February 2010 (UTC)

Morality And The Scenario Of PD

If PD is formulated as a scenario of persons suspected of a crime, one might make a game-theoretical explanation of morality regarding PD clearer by eliminating the crime element from the consideration/discussion. That is, shouldn't the morality of PD behaviors be explicitly described as relating to the narrow context of the two prisoners' treatment of one another, rather than left to possible interpretation as relating to the crime itself? Cooperation in crime is usually considered immoral. It's not a needful clarification for folks looking at the matter with the typical eye of someone deeply studying it, but for the casual reader it could help. —Preceding unsigned comment added by 63.249.110.34 (talk) 18:20, 24 May 2010 (UTC)

Mathematicians have no godfather?

The article suprisingly makes no mention of the words mafia, cosa nostra, omerta, onesta, blood revenge, even though these show the prisoner's dilemma simply doesn't exist in real life. People who divulge about the Family can expect to see themselves or their relatives slaughtered by the mafia, thus everybody remains silent when facing cops or judges. The other criminal is your brother and the authorities are your enemies, thus comes the rule of omerta.

This has been going on for centuries in Sicily and Corsica and the mafia has never been successfully dismantled (except for the Mussolini era, when ALL men between 14-50 were thrown into prison camps by military force without any investigation. They didn't need or want confessions then...) 87.97.52.2 (talk) 09:22, 26 June 2010 (UTC)

As this is a topic in mathematics, it is discussed from a mathematical point of view. Like all problems, it is an idealization and not supposed to reflect reality. You may as well say that chess "doesn't exist in real life" because real soldiers don't take turns. Eebster the Great (talk) 02:36, 28 June 2010 (UTC)

Confusion

This is confusing to read because if you are familiar with the law you know the term "cooperate" means to rat or betray. Maybe it should say remain silent, mute, or ask for a lawyer. —Preceding unsigned comment added by 24.228.187.104 (talk) 05:50, 3 January 2011 (UTC)

Generalized form

Why doesn't the generalized form mention prisoners? Isn't the version with two prisoners a more common form of the dilemma? MCSKY (talk) 23:20, 23 July 2010 (UTC)

Because the "generalized" is made to be more general, i.e. to cover a general situation (which does not necessarily refer to prisoners) rather than being restricted to a specific situation involving prisoners. JamesBWatson (talk) 08:29, 26 July 2010 (UTC)

Maasai of East Africa

It appears that the paragraph regarding the Maasai of East Africa is made in good faith. I am removing it, not because I believe it to be in bad faith, but because I believe that it needs quite a bit of work, and is, unfortunately, confusing in its current form. By deleting the paragraph, I hope to spur authors to restore it, in better shape. (See Wikipedia:BRD.)

In the deleted paragraph, reproduced below, terms such as "cyclical age system," "Theory of Dilemmas," and "Rebel’s Dilemma" are used in such a way that a reader may think that they have already been described in the article. Alas, they have not been, nor are they defined anywhere in Wikipedia. I am hopeful that we can somehow give the reader some idea as to what these terms mean.

Also, the existence of a "resolution to the paradox of the Prisoner’s Dilemma" certainly deserves more ink. What are some of the details?

The deleted paragraph is:

The dynamics of the cyclical age system among the Maasai of East Africa may be examined in terms of a Theory of Dilemmas, tracing through a series of non-zero-sum games, leading to a catastrophic switch in each cycle. These ‘games’ include Cat and Mouse, Chicken, Prisoner’s Dilemma, and Rebel’s Dilemma. The Rebel’s Dilemma (in an insurrection) offers a resolution to the paradox of the Prisoner’s Dilemma, which otherwise points towards universal mistrust in human interaction as opposed to faith. The concept of Providence lurking behind the Theory of Dilemmas is also expressed in Maasai thought and cosmology.

Thank you —Quantling (talk | contribs) 19:33, 25 January 2011 (UTC)

The "Strategy" section seems confusing (to this layman)

It says "In this game, regardless of what the opponent chooses, each player always receives a higher payoff (lesser sentence) by betraying". This just seems wrong to me (only a layman in regards to game theory), because if the opponent chooses to cooperate, then I receive a higher payoff if I also cooperate. I think you meant to say "not knowing what the opponent will choose, each player lessens their chance of receiving the lowest payoff (greatest sentence) by betraying". There is a distinct difference, at least when it comes to prison sentences. 75.52.255.18 (talk) 09:48, 7 February 2010 (UTC)

Suppose you know the other prisoner is going to cooperate. If you cooperate, you will get a six month sentence, but if you betray, you will go free. Therefore you should betray. Suppose, however, you know the other prisoner is going to betray. If you cooperate, you will get a ten year sentence, but if you betray, you will get only a five year sentence. Therefore you still should betray. So regardless of what the other prisoner will do, you should betray. Eebster the Great (talk) 17:48, 7 February 2010 (UTC)

I actually wondered about the same thing - I have a pretty good grasp on PD and Game Theory, but I seem to remember this article having a section with examples from popular culture (e.g. in The Dark Knight the Joker strands two ferries full of people offshore and tells them both that they have the triggers to bomb the other ferry). These kinds of examples resonate with many folks and aid in understanding -I don't know why they aren't here. Anyone know? Cknoepke (talk) 19:55, 8 February 2011 (UTC)

There's things which might seem trivial, but make it so the Joker-Ferry scenario isn't actually a prisoner's dilemma, so it's not a good example. Another example from popular culture might be good, but would be best if it was not just recognized by a WP editor, but by another reliable source. CRETOG8(t/c) 23:47, 8 February 2011 (UTC)

Cournot

I know that of course the situation described by the game predates its formalization, but it seems to me that Cournot's famous 1840's oligopoly model should be mentioned since it describes a Prisoner's dilemma situation and even solves for the Nash equilibrium. Volunteer Marek  00:57, 10 February 2011 (UTC)

Courtnot's model is a bit dilemma-ish, but I don't think it's really a prisoner's dilemma, since the players don't have dominant strategies. This possibly goes along with the continuous strategy space, where the clearest PD examples have few discrete strategies. CRETOG8(t/c) 01:20, 10 February 2011 (UTC)

Yes that's right - a typical presentation in an undergrad textbook in fact has Cournot as a prisoner's dilemma (since can't ask undergrads to derive reaction functions), dominant strategies and all. It's true - IIRC - that Cournot himself considered the continuos case. I'm not sure if extensions of the basic PD to the continuos strategies case in general still implies some kind of strictly dominant strategies. Volunteer Marek  02:05, 10 February 2011 (UTC)

TO COOPERATE IN THIS SENSE MEANS TO BETRAY

TO COOPERATE IN THIS SENSE MEANS TO BETRAY, WHEN A PERSON IS ARRESTED FOR A CRIME HE CAN CHOOSE TO EITHER 'COOPERATE' AS IN WITH THE AUTHORITIES AND GIVE UP HIS ACCOMPLCE, OR EXERCISE HIS RIGHT TO STAY SILENT, OR REFUSE TO COOPERATE, AND NOT RELEASE ANY INFORMATION. THIS ARTICLE IS NOT WORDED PROPERLY. —Preceding unsigned comment added by 69.117.219.63 (talk) 10:14, 1 May 2011 (UTC)

The Wikipedia editor's dilemma

In an on-line encyclopaedia where anybody can edit almost any article each editor is faced with a dilemma: should they help write a succinct article using terms and phrases which ordinary members of the public can easily understand, so best to educate the masses, or should they use as many technical terms as possible to demonstrate their own extraordinary mastery of the subject at the expense of clarity for the masses. This is a sub theory of game play which has yet to be explored fully. — Preceding unsigned comment added by 81.187.233.172 (talk) 18:24, 25 May 2011 (UTC)

Alternate Dilemma

I was told that the Prisoner's Dilemma goes like this: There is no evidence on each prisoner. So, the first prisoner that talks gets three months in jail, while the other gets one year in jail. But if both stay silent, they both go free because there is no evidence. In this context, it's a matter of mutual trust. There is obviously no "both talk" scenario because only one confession is needed. Corwin8 (talk) 16:39, 11 July 2011 (UTC)

It's a simultaneous move game. They both talk. If it's a "who goes first" game then they both talk immediately. Whether one or two confessions is needed is immaterial.Volunteer Marek (talk) 17:21, 11 July 2011 (UTC)

Flaw

The front page says the flaw is that the punishment for both staying silent should be zero jail time. However, what if the police had enough evidence to support manslaughter but not to support murder. In comes the prisoner's dilemma. Also, is the result of staying quiet not only important in that it must be less time in jail than defecting?98.95.129.142 (talk) 00:29, 1 January 2012 (UTC)

Axelrod's tournament

Most of the text from the mistitled "Strategy for the classic prisoner's dilemma" needs to be either removed or moved to its own separate article. This article is supposed to be about the general concept of the Prisoner's dilemma, NOT about Axelrod's tournament in particular, and certainly not a forum for a discussion which strategy program is the best (I will note at this point that obviously, since contestants can submit multiple entries, strictly speaking the tournament itself IS NOT a Prisoner's dilemma, and it seems that the Jennings group simply recognized this fact and adjusted accordingly).

On a more general note it seems the article has acquired much useless cruft, trivia, individual opinion and other nonsense. As a consequence I'm going to down grade it to C-class. Which is too bad since this was once a FA.Volunteer Marek (talk) 05:56, 18 June 2011 (UTC)

The section "Strategy for the classic prisoner's dilemma" should surely be named "Strategy for the iterated prisoner's dilemma" 80.254.147.84 (talk) 08:59, 12 January 2012 (UTC)

prisoners' dilemma

this should be properly referred to as the Prisoners' Dilemma. No dilemma without two prisoners, and the dilemma applies to each and the rational choice issue that comes up. — Preceding unsigned comment added by 24.207.227.55 (talk) 18:32, 15 August 2011 (UTC)

No, it's correct. "The prisoner" refers to a class of people, not two prisoners in particular. Also virtually every reference calls it "the prisoner's dilemma." 18.189.110.147 (talk) 06:57, 15 December 2011 (UTC)

In its current form, the article is inconsistent in its placement of the apostrophe. Based on the discussion above, it should consistently be "the prisoner's dilemma." 80.254.147.84 (talk) 08:58, 12 January 2012 (UTC)

About Criticism (bottom of the page)

So my little intervention got wiped out as I was expecting, but anyway there is a lot of truth in my explanation, and I reword it in a shorter way : "If the collectivity (in this case the 2 prisoners) does not find the best deal, something is wrong!" But why does it happend so often in real life ? Answer : lack of information and analyse to obtain the best global soultion! I also think the result of prisonner related games depend strongly on the personality of the player andtherefor the dilema does not always hold, and I think this should be specified in the main article! Sorry I got no references, but it's probably possible to find some. — Preceding unsigned comment added by 144.85.164.102 (talk) 21:56, 4 June 2012 (UTC)

Regardless of what the other prisoner chooses...

I've pointed this out before, as has at least one other user, but the following sentence is nonsense:

"Regardless of what the other prisoner chooses, one will always gain a greater payoff by betraying the other."

In fact the very next sentence (if taken to be factually correct) proves this:

"Because in *almost* all solutions..."

Please can't we just delete the first sentence? I'm perplexed that the people editing this article can't recognise this basic error.

Edit:

Perhaps something along these lines would be do:

"If the prisoners are unintelligent and we assume that they will behave according to their intrinsic desire to better their situation (at the expense of others if necessary), then they will tend to betray.

However if the prisoners are both intelligent they will deduce that 1. the best option is to cooperate, and that 2. the other prisoner will also realise this, and hence both will choose to cooperate.

Where one prisoner is intelligent and one is not, the unintelligent prisoner will tend to betray, while the intelligent prisoner will likely begrudgingly betray also."

— Preceding unsigned comment added by 61.19.65.160 (talk) 22:11, 9 November 2011 (UTC) 

That doesn't work. Defection is a dominant strategy. If the other person cooperates, you're better off defecting. If the other person defects, you're better off defecting. Therefore, you're better off defecting. That's the essence of what makes the game interesting. Other things which make the game interesting are the many ways that people sometimes avoid this bad dynamic, which is discussed, maybe not ideally in the article. But the text, "Regardless of what the other prisoner chooses, one will always gain a greater payoff by betraying the other." is correct. CRETOG8(t/c) 00:33, 10 November 2011 (UTC)

Thank you! Finally somebody's explained it clearly. I now understand how the sentence makes sense. What I now DON'T understand is how the prisoner's dilemma is of any consequence, as it doesn't appear to apply to our reality. But I suppose that's irrelevant. Thanks for your reply. — Preceding unsigned comment added by 61.19.65.89 (talk) 19:29, 13 November 2011 (UTC)

Neither does Poker, but we play it anyhow.98.95.129.142 (talk) 00:32, 1 January 2012 (UTC)

"Defection is a dominant strategy. If the other person cooperates, you're better off defecting. If the other person defects, you're better off defecting. Therefore, you're better off defecting."

I think the quote above from CRETOG8, though less rigorously stated, is a clearer explanation than the first paragraph of the first section ("Here, regardless of what..."). If possible, perhaps it can be integrated into that section of the article. 108.202.195.150 (talk) 02:01, 25 February 2012 (UTC)

Title

Should it be "prisoners' dilemma" (plural) rather than "prisoner's dilemma"? Surely the dilemma only arises when there is more than one prisoner. — Preceding unsigned comment added by 129.105.50.254 (talk) 16:02, 25 April 2012 (UTC)

I disagree. Logically speaking, each prisoner ultimately makes the decision for himself/herself -- potentially influenced by the situation or the decisions of others. Gprobins (talk) 13:45, 22 July 2012 (UTC)

Criticism

The top section needs to be edited for inaccuracy. It states: "In the regular version of this game, collaboration is dominated by betrayal, and as a result, the only possible outcome of the game is for both prisoners to betray the other. Regardless of what the other prisoner chooses, one will always gain a greater payoff by betraying the other. Because betrayal is always more beneficial than cooperation, all objective prisoners would seemingly betray the other if operating purely rationally." One will NOT always gain a greater payoff by betraying the other; that will be true only if the other prisoner doesn't rat me out. The problem here is the method of reasoning one uses to calculate one's course of action. As the following section explains, if one reasons as follows. "My partner has two choices: rat me out or stay silent. If he rats me out, then I'm better off ratting him out. And if he stays silent, then I'm better off ratting him out. Therefore I should rat him out." But this line of reasoning ignores the fact that there are four possible outcomes, not two, even though I have only two choices. If I'm willing to gamble that my partner might be silent, then it is rational for me to remain silent too, even though this places me at greater risk of betrayal. The whole point of the dilemma is that it's a paradox that can't be resolved by the binary reasoning mentioned above. It's simply not true that each prisoner is catagorically better off by betraying the other, because if my partner rats me out, then I give up the possibility of a one-month sentence for the surety of the 3-month sentence. ~Leghorn — Preceding unsigned comment added by Leghorn (talk • contribs) 19:22, 7 September 2012 (UTC)

I just added this paragraph, which seems necessary for a real life approach, what an ugly world otherwise, by the way it's quite right, the P dilemma is a dilemma only with enough stupidity or a strong desire to hurt the other no matter what the consequences! It happens quite often and can be tested with another "game" where people need to share money and decide how! Don't remember the name of that game.

It's not a dilemma anymore if you got enough trust between the actors or just enough will to be as little hurting as possible for the other, in these cases it's always the best global scenario that get in (both get a short time in jail and after that they can laugh about it). In real life on the other hand hoping for immediate freedom when sending the other a long time in jail could be risky for the "winner" because of possible post culpability and retaliation. This show us that the prisoner's dilemma apply in some narrow scenario where actors are unable to analyze the full realm of possibilities, this is also obvious with environmental CO2 issues where changing life style is just viewed as an annoyance when it's really an opening to new opportunities and healthier life style! For example the actual obesity crisis is partly in such an amplitude because of CO2 issues (if people were less dependent on motorized mode of transportation they would be obviously fitter, eg : walking or cycling around). — Preceding unsigned comment added by 144.85.164.102 (talk) 14:52, 4 June 2012 (UTC)

There is something to what you say, and people do research those points. For instance, Elinor Ostrom mentioned in the section risoner's_dilemma#Multiplayer_dilemmas has studied resource dilemmas and find a lot of circumstances where things don't work out so badly. However, since the prisoner's dilemma has been studied lots in lots of contexts, off-the-cuff analysis isn't appropriate for this article. It should describe analysis already done by others. CRETOG8(t/c) 23:57, 4 June 2012 (UTC)

The Prisoners' Dilemma is a theoretical model of human strategic behavior only. It holds under certain conditions like individualism, utility maximization behavior, etc. Check behavioral game theory and/or experimental economics related topics for the real-life results. — Preceding unsigned comment added by 87.205.165.178 (talk) 16:34, 29 August 2012 (UTC)

I agree with the previous statement. Unless I'm seriously mistaken, the Prisoner's Dilemma is an interesting property of certain games named after an appropriate example, as opposed to a direct problem that's subject to criticism due to the means used to describe it. JaeDyWolf ~ Baka-San (talk) 19:17, 29 August 2012 (UTC)

Security Issue

I don't know how else to report this so I'm writing it here and hopefully somebody will notice. I googled 'prisoners dilemma' and clicked on the first link which said it would take me to en.wikipedia.org/wiki/Prisoner's_dilemma (both in the green text under the blue search result as well as in the status bar when I moused over it) but instead forwarded me to this url: http://www.happili.com/bc_rus3/innerxy.php?q=prisoner%27s%20dilemma&xy=bcr3 I don't know how to fix this or what the problem even is. I hope somebody does. — Preceding unsigned comment added by 50.138.165.255 (talk) 03:55, 4 March 2012 (UTC)

I suspect it is something to do with your computer/browser. I googled the same as you did and did not find any such link on the first page of results. You might run some reputable malware/spyware/virus removal tools, try a different browser and/or different computer to try to isolate and solve the issue. — Safety Cap (talk) 18:41, 21 January 2013 (UTC)

What Prisoner's Dilemma Shows

The lede says that the Prisoner's Dilemma "shows why two individuals might not cooperate, even if it appears that it is in their best interest to do so". That doesn't seem like an accurate description. What it actually shows is that pursuing logically self-interested outcomes is not always Pareto Optimal. That was the point of this theory being put forward. Poyani (talk) 12:57, 15 August 2012 (UTC)

Citation issues?

Apparently there is an issue with the citation style, yet I am looking at the footnotes and I cannot figure out what needs to be fixed. Can anyone clarify? — Carrot Lord (talk) 01:37, 16 January 2013 (UTC)

Yes, the citations are bare and not formatted with metadata. Many citations are of this form:

<ref>Camerer C. 2003. Behavioral game theory. Princeton: Princeton University Press.</ref>

Ideally, they should be like this:

<ref>{{cite book | title=Behavioral game theory. | publisher=Princeton University Press | author=Camerer, C. | year=2003 | ...

It will take a bit of work to determine if the reference is a book, journal, website, etc. Googling the title + author name is usually enough to get the original source (Google books sometimes have book citation information at the bottom of some of their books' info pages) — Safety Cap (talk) 19:11, 21 January 2013 (UTC)

Snowdrift = Chicken

Did anyone notice that the snowdrift game on the bottom of the page is also a version of Chicken (game)?

174.67.247.165 (talk) 04:20, 24 January 2013 (UTC)

"Cooperates" - terminology

I found the term "cooperates" a little confusing at first, mainly because it is used more commonly as: "the prisoner cooperates with the police" - the exact opposite to the meaning in the article. It is also not a good antonym for "betrays". A better term might be "remains loyal". — Preceding unsigned comment added by 157.189.16.194 (talk) 04:22, 14 February 2012 (UTC)

Exactly what I was thinking. Perhaps "collaborate" is a suitable replacement? It definitely does not have the same police connotation. — Preceding unsigned comment added by 141.166.209.17 (talk) 02:04, 15 December 2012 (UTC)

I agree too. The lead section talks about confessing or denying the crime. The first sub-section talks about cooperating or defecting. It is hard to tell which matches with which. Is "cooperating" cooperating with the police by confessing or is it cooperating with the other and denying the crime? How about clarifying the terminology and making it easier to follow through the article.

And then there is confusion between confessing to the crime, denying the crime, and saying that the other one did it. Bubba73 ^{You talkin' to me?} 05:29, 19 October 2013 (UTC)

Different payoffs

I'm no game theorist by any means but there is something very unsettling about this game and I think it has to do with the way the payoffs are designated for each player. I think this is a better payoff matrix:

	Prisoner B stays silent (cooperates)	Prisoner B betrays (defects)
Prisoner A stays silent (cooperates)	Both go free	Prisoner A: 3 years Prisoner B: 1 year
Prisoner A betrays (defects)	Prisoner A: 1 year Prisoner B: 3 years	Each serves 2 years

In this case, if both players keep quiet they both go free given that the police has no evidence to convict them. If they both confess they both get 2 years (just as in the original matrix). If one of them confesses while the other keeps quiet, the one that betrays should be "rewarded" by getting a lesser sentence (but not go free) and the one that stays silent should be "punished" by getting an extended sentence.

In payouts notation:

Example PD Payouts (A, B)

	B cooperates	B defects
A cooperates	200, 200	-100, 100
A defects	100, -100	0, 0

What would be the equilibrium in this case? Is this a different game? Maybe I'm a bad guy who just wants the criminals to get away... — Preceding unsigned comment added by 201.171.99.55 (talk) 18:47, 15 September 2013 (UTC)

That would indeed be a different game. Your payoff matrix doesn't conform to the T > R > P > S requirement for it to be a PD, because T < R. Binkyuk (talk) 15:41, 8 January 2014 (UTC)

Yes, and the consequence of T<R is that cooperation is always guaranteed for "rational" players. If both players are trying to maximize their income (or freedom) and both know it, they will always cooperate. PAR (talk) 04:40, 3 July 2014 (UTC)

Because...

"Because betraying a partner offers a greater reward than cooperating with them..."

But in one scenario it also offers a greater downside doesn't it? Might it be better written as:

"Because betraying a partner offers ON AVERAGE a greater reward than cooperating with them..."?

But that still doesn't make sense, as either version suggests that whatever course of action is chosen, it will result in a 'reward'. So maybe something like:

"Because betraying a partner results, on average, in a lighter sentence..."? — Preceding unsigned comment added by 49.49.24.98 (talk) 22:26, 20 March 2014 (UTC)

In both the case where your opponent cooperates and defects, defecting gives a higher personal payoff than cooperating (0 years vs 1 year if they cooperate, 2 years vs 3 years if they defect). No "on average" required. Binkyuk (talk) 09:57, 3 July 2014 (UTC)

New findings

I don't have the grasp needed to change the article, but this deserves a look https://www.quantamagazine.org/20150212-game-theory-calls-cooperation-into-question/ — Preceding unsigned comment added by Trilobite12 (talk • contribs) 17:27, 21 February 2015 (UTC)

The cause of the apparent dilemma in people's actions

Actually, the one-round prisoner's dilemma is ONLY a dilemma if the agents are completely self interested. Altruistic rational agents in a one-round prisoners dilemma would both chose normally to cooperate.

Let the players be A and B. As both are altruistic, they value their (shared) payoff as the sum of all involved payoffs. Also adopt the form discussed, where -1 is the mutual cooperation payoff, 0 is the defect-while-opponent-cooperates payoff, -3 is the cooperate-while-opponent-defects payoff and -2 is the mutual defection payoff.

Now, if B defects, examine A's choices. If he defects, the total payoff is -4, whilst if he cooperates, the total payoff is -3. If B cooperates and A defects, the total payoff is -3, while if A cooperates the total payoff is -2. So whatever B does, an altruistic player is better off co-operating.

As in the real world players are likely to be a mix of self-interested and altruistic, this explains the mix of outcomes given when people attempt to test the prisoner's dilemma. Consider adding this to the 'Prisoner's Dilemma' main page. — Preceding unsigned comment added by Anticontradictor (talk • contribs) 01:06, 8 December 2015 (UTC)

real life examples

Shouldn't the real life examples include, you know, the actual scenario on which the original PD is based? like prosecutors/cops and suspects in, eg, the US legal system? — Preceding unsigned comment added by 68.65.169.68 (talk) 01:14, 6 April 2014 (UTC)

In real world, there is probability the criminal gang would retaliate against the betrayer who was set free at partner's expense.

First, no one expects the real world example to fit the model perfectly; it's an approximation. Second, this deviation from the model you mention isnt essential to the OP's scenario (it might not be gang-related, witness protection etc). Third, the retaliation might not offset the incrementally better sentence from snitching. I think the OP has a point. "Prisoner's dilemma" doesn't seem like one of those labels that's a complete misnomer; it could turn up in cases of actual prisoners in a given legal system. Snarfblaat (talk) 00:32, 5 November 2014 (UTC)

I think the real-life example around "guppies" and tit-for-tat is from Axelrod & Hamilton: http://www.life.umd.edu/faculty/wilkinson/BIOL608W/Axelrod&Hamilton81.pdf They don't metion "guppies", per se, and I don't even know if that species of fish exhibit this behavior, so I didn't make the citation myself. The relevant part of the paper, following an overview of tit-for-tat is "Another mechanism to avoid the need for recognition is to guarantee the uniqueness of the pairing of interactants by employing a fixed place of meeting. Consider, for example, cleaner mutualisms in which a small fish or a crustacean removes and eats ectoparasites from the body (or even from the inside of the mouth) of a larger fish which is its potential predator. These aquatic cleaner mutualisms occur in coastal and reef situations where animals live in fixed home ranges or territories (4, 5). They seem to be unknown in the free-mixing circumstances of the open sea." However, this paper is cited by Morton D. Davis of a real-world example of tit-for-tat by fish cleaning parasites off predators in "Game Theory: A Nontechnical Introduction" ISBN 0486296725 Tearaway (talk) 20:57, 14 February 2016 (UTC)

Use in Storytelling

I feel as if this has been used extensively in storytelling over the decades since it was developed, and likely even before that. However, the example that I thought of as soon as I read the article is the ferry boat scene from The Dark Knight. In this scene, there are two ferries that have sailed from Gotham, one full of everyday commuters and the other full of prisoners from the city jail. Mid-crossing the power to both ferries is cut and the Joker explains that both ferries are wired to explode. Each ferry has a detonator for the other ferry. All they need to do is use it, destroy the other ferry, and they will be saved. In the film both sides decide to not detonate the bombs, trusting the other passengers in the other ferry to do the same. Unless I see any objections to this use of the Prisoners Dilemma I will add it to the page in a couple of weeks. Editengine (talk) 01:32, 9 February 2016 (UTC)

Added the storytelling section. Editengine (talk) 12:46, 18 February 2016 (UTC)

Dr. Duffy's comment on this article

Dr. Duffy has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

A rambling mess. No mention of dominance, Nash equilibrium or the uniqueness of the Nash equilibrium in the game form. "A very narrow interpretation rationality" is a weak, subjective statement. Indeed rationality in the context of this game is not defined but simply involves each player playing a best response to the payoff incentives of the game.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Duffy has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : John Duffy & Huan Xie, 2012. "Group Size and Cooperation among Strangers," Working Papers 12010, Concordia University, Department of Economics.

ExpertIdeasBot (talk) 16:56, 19 May 2016 (UTC)

Removed the vague mention of "restrictive interpretation of rationality" and moved the discussion of dominance and nash equilibrium up a section to be more prominent (though it was there in the General Form section), but I don't think it fits in the (already quite long) lede. Binkyuk (talk) 14:46, 16 December 2016 (UTC)

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