Have prisoners learned not to snitch?

27th July, 2013

“They finally tested the ‘prisoner’s dilemma’ on actual prisoners – and the results were not what you would expect”
BusinessInsider.com, July 21

It is amazing that it has taken six decades to get around to testing out the prisoner’s dilemma on real prisoners.

Is it? The prisoner’s dilemma is a little fable economics teachers use to make a formal example more memorable. It was never actually a prediction of how prisoners behaved. Presumably you also think it’s remarkable that two and a half thousand years after Aesop, nobody has got around to re-enacting “the Tortoise and the Hare” with a real hare?

Grumpy today, aren’t we?

Well, I do feel that the prisoner’s dilemma has unjustly monopolised the popular imagination of what game theory is all about. Game theory attempts to analyse situations where a few people interact in such
a way that they need to take each others’ behaviour into account. The prisoner’s dilemma is just one such example.

Why has it garnered so much interest?

Partly because it seems to produce a paradox, and partly because there’s a good story to go with it. Two suspects are charged with a serious crime, carrying a sentence of 20 years. There’s only enough evidence to convict them of something more trivial, with a sentence of two years. The prosecutors tell each prisoner that if he confesses to their joint guilt, his sentence will be halved. Furthermore, if he confesses and the other prisoner is silent, he won’t even be charged with the more serious offence.

Hang on, let me get a pencil.

The prisoner’s dilemma, then, is that you get one year if you confess and the other guy stays silent, two years if you both stay silent, 10 years if you both confess and 20 years if you stay silent and the other guy confesses. The apparent paradox is that no matter what the other prisoner does, you will improve your own situation by confessing – yet as a pair the prisoners would be much better off if they could somehow both commit to remain silent. So the dilemma is seen to symbolise all sorts of problems of social co-operation.

You seem sceptical.

Well, the prisoner’s dilemma has a dark beauty to it but as a model of real life it’s not great – when the game is changed so that the prisoners are put in the same situation repeatedly, for instance, the results change. A less famous game, known as the “stag hunt”, is often a better model for the difficulty of co-operating. A run on a bank is not much like a prisoner’s dilemma but a lot like a stag hunt.

Are you not curious to know what the prisoners did when faced with the prisoner’s dilemma?

Oh, I certainly am curious – curious enough to look up the research. The researchers, Menusch Khadjavi and Andreas Lange, conducted low-stakes prisoner’s dilemma experiments both with female prisoners and female students. The headline-grabbing result: prisoners co-operate with each other more than students do.

What does that tell us – that prisoners take care of each other? Or that they fear reprisals?

Probably not reprisals: they were promised anonymity. It’s really not clear what this result tells us. We knew already that people often co-operate, contradicting the theoretical prediction. We also know, for instance, that economics students co-operate more rarely than non-economists – perhaps because they’ve been socialised to be selfish people, or perhaps because they just understand the dilemma better.

You think the prisoners just didn’t understand the nature of the dilemma?

That’s possible. The students were much better educated and most students had played laboratory games before. Maybe the prisoners co-operated because they were too confused to betray each other.

That seems speculative.

It is speculative, but consider this: the researchers also looked at a variant game in which one player has to decide whether to stay silent or confess, and then the other player decides how to respond. If you play first in this game you would be well-advised to stay silent, because people typically reward you for that. In this sequential game, it was the students, not the prisoners, who were more likely to co-operate with each other by staying silent. So the students were just as co-operative as prisoners but their choice of when to co-operate with each other made more logical sense.

First published on FT.com.

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