Why Do Prisoners Cooperate in the Prisoner’s Dilemma?

According to a new study by Menusch Khadjavi and Andreas Lange, prisoners cooperate more frequently in prisoner’s dilemmas than college students. Here’s the abstract from their article “Prisoners and Their Dilemma”:

We report insights into the behavior of prisoners in dilemma situations that so famously carry their name. We compare female inmates and students in a simultaneous and a sequential Prisoner’s Dilemma. In the simultaneous Prisoner’s Dilemma, the cooperation rate among inmates exceeds the rate of cooperating students. Relative to the simultaneous dilemma, cooperation among first-movers in the sequential Prisoner’s Dilemma increases for students, but not for inmates. Students and inmates behave identically as second movers. Hence, we find a similar and significant fraction of inmates and students to hold social preferences.

I have always thought that the prisoner’s dilemma was a terrible example of strict dominance for introductory classes in game theory. Students tend to shoot back with “snitches get stitches” or something similar, so prisoners would cooperate in such a situation. This leads to an awkward conversation about expected utilities when all you really want to do is explain the logic of strict dominance. The study further suggests we drop the prisoner story from the prisoner’s dilemma.[1]

Nevertheless, after having read the article, I have serious problems with the results. The article is extremely short on theoretical mechanisms, so I am going to step in and provide some speculation. Here are three explanations for the result:

  1. The mechanism the authors would prefer is that prisoners are incredibly strategic. To quote Red from Shawshank Redemption, prison time is slow time. Prisoners have nothing better to do than plot, strategize, and scheme against one another.[2] While this might initially appear detrimental to cooperation, the truth is just the opposite. Everyone knows you can’t get away with doing stupid things, so people don’t bother. As such, prisoners cooperate–even though the game is anonymous, cooperation is less likely to lead to a witch hunt later and less likely to cause problems greater than a few Euros worth of phone credit.
  2. Prisoners didn’t believe that the game really is anonymous. The experimenters stressed to participants that they would be the only one to see the results. However, this is utterly ridiculous. No one, NO ONE, NO ONE took that statement at face value. Marek Kaminski, a political scientist at UC Irvine, spent some time in a Polish prison for publishing anti-communist materials way back in the day. He wrote Games Prisoners Play based off of his experiences.[3] It is a compelling read. Kaminski might be the only serious social scientist to spend time in a prison. He makes a big point that we really shouldn’t trust any studies of prisoners simply because prisoners do not trust supposedly confidential experimenters. At all. Prisoners might have cooperated in the study because they believed the prison staff would see the results, or other prisoners would see the results, or whatever. College students, meanwhile, know the results will be confidential and are therefore free to defect all they wish.
  3. The results have nothing to do with the prison/free dichotomy but rather education levels. Non-prisoners in the study were all college educated. The prisoners averaged below 10 years of schooling. The authors only obtain statistically significant results without any controls. Once they popped in education level, the only thing that was statistically significant was coffee consumption. (Good luck explaining that result theoretically!) But education and the prisoner dummy are about as multicollinear as multicollinearity gets. We probably shouldn’t trust the coefficients on either of those variables. But this also would mean that education would be statistically significant if you ran a regression without any controls. Perhaps the prisoners just don’t see that defection strictly dominates cooperation. The data tell us nothing here.[4]

On the surface, the paper is neat. However, authors of any quantitative model need to think hard about their data generating process and then construct their research design model accordingly. The authors don’t do that here, especially when it comes to point 3. As such, this study is…lacking.

[1]But this is a coordination problem, and we are well past that tipping point.
[2]This is why Orange Is the New Black is an interesting series.
[3]The authors do not cite Kaminski. It should be required reading (and a required citation) for all studies of prisoners.
[4]I would imagine someone has previously studied the effect of education level on prisoner’s dilemma cooperation, but I am unaware of any such study and the authors do not cite any.

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