# The Prisoners’ Dilemma

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The Prisoners’ Dilemma

The Prisoners’ Dilemma- I would imagine it is the most well known game theory idea. People who know very little about game theory, or think they know very little about game theory still have probably at least heard of the “prisoner’s dilemma”. But, I believe it was Dixit and Nalebuff who pointed out it should be referred to as the Prisoners’ Dilemma, as there is no dilemma without at least two people.

So, it involves at least two people, but what else? Well, literature and websites about the prisoners’ dilemma abound. I’m not even really going to go to far in depth on what it is, many others have already covered that. Like here from Stanford Philosophy, here where you can play a Prisoners’ Dilemma (PD), here, and also here.

But, here’s the thing. I don’t really like the narrative of the prisoners’ dilemma anymore. When I first learned about it I did sort of. But, not anymore. The narrative is usually something like this: two people are arrested and the cops are trying to get them confess. And then a bunch of complicated things about sentencing and ratting people out and other stuff.

It’s not really relevant and I think adds too much to the example. I end up getting hung up on minor details about the criminal justice system as opposed to appreciating what the Prisoners’ Dilemma is supposed to illustrate. So here’s an easier way to think about it:

as taken from “Rational Cooperation in the Finitely Repeated Prisoner’s Dilemma: Experimental Evidence” by Adreoni and Miller, which I plan to blog about in the future. But it gets the point across.

In a PD, you can either cooperate or defect (aka betray-although that is such a loaded word). Your partner does the same. You can’t talk to each other. That payoff table shows what happens. The both left of each square is what you could get: 0, 4, 7, or 12.

So, you obviously want 12 the most. You’ll have to defect against the other guy though. Not only that, but he will have to play cooperate in order for you to get 12. But then he will get 0!

Playing defect will always get you more than playing cooperate, which means that the defect strategy dominates the cooperate strategy. But, and herein lies the dilemma, if both of you defect, you do worse off than if you both cooperated!

So, you should both cooperate then! But, if your opponent should cooperate, then you should defect to take advantage of his/her cooperation. But, they should do the same thing to you! Then you are back to the vicious defect cycle.

It can make you go a little crazy trying to “solve” the prisoners’ dilemma. But maybe it doesn’t need to, or in fact cannot be solved. For right now, I’m striving for understanding of it. I think a PD illustrates some good points about game theory stuff in general:

- It’s all about interactions with other people. It’s a prisoners’ dilemma, not the dilemma of a single prisoner. A one person game doesn’t really exist. It’s about chess and checkers, not solitaire.
- It’s about strategy- which in turn is about planning for what your opponent is doing, which is probably based on what you are doing.
- It has a lot of loaded words and concepts like “opponent”, “betray”, “defect”, “trust”, “greed” and “dilemma”. You might be less likely to cooperate with someone labeled your opponent versus your friend.
- Games can be played once and never again, or be repeated up to infinity. This is something I will be looking at later (maybe next), in the form of the oh so interesting Axelrod tournament.

But, nevertheless I post this just to introduce the Prisoners’ Dilemma as I am sure I will be referencing it a bunch. Much better and more thorough examples of PDs exist in the above links.

Picture Credit: First picture taken from here.

Posted on August 15, 2011, in Uncategorized and tagged game theory, mixed motive game, prisoners' dilemma, utility. Bookmark the permalink. 6 Comments.

Concerning the apostrophe: On the one hand, as dguenther says, it’s a dilemma resulting from the interaction of two players, hence the preference for “prisoners’ dilemma” (plural). On the other hand, the game presents a dilemma for EACH INDIVIDUAL prisoner, although it is absolutely clear what is best (mutual cooperation, of course) for the PAIR of prisoners. Hence in that sense, “prisoner’s” dilemma (singular) would be preferred. Either argument really focuses attention on the conundrum at the heart of the PD. So from a pedagogical standpoint, the punctuation argument is an instructive one either way!

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