Talk:Prisoner's dilemma

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[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)
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)


[edit] 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)


[edit] 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)


[edit] 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 2 "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 3, 3 4, 0
Defect 0, 4 1, 1

C gets whatever is left.

So the payoff for defecting is 4 instead of 5. This is to remove bias from the game. If I were to leave it at the original 5, the game would be biased 8.33% against player C.

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 +1, +1, -2 +2, -2, 0
Defect -2, +2, 0 -1, -1, +2

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)

[edit] 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)


[edit] 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)

[edit] 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)