The prisoners' dilemma, with real prisoners (and the Camorra)

I've written a number of posts about the prisoners' dilemma (most recently here). In the prisoners' dilemma, all players have a dominant strategy, which is a strategy that is always better for the player, no matter what any of the other players choose to do. However, if each player acts in their own self-interest, the outcome leads to payoffs that are worse for everyone, than if they had cooperated. Robert Frank has described these games as leading to behaviour that is 'smart for one, dumb for all'.

There have been a number of studies of decision-making in the prisoners' dilemma. It is an important game to study, because it can tell us a lot about cooperation, particularly when we compare different population groups. Following that theme, this 2018 article by Annamaria Nese, Niall O’Higgins (both University of Salerno), Patrizia Sbriglia (University of Campania Luigi Vanvitelli), and Maurizio Scudiero (Ministry of Justice, Italy), published in the journal European Economic Review (ungated earlier version here), compares behaviour in the prisoners' dilemma between ordinary prisoners, Camorristi (Mafiosi from Naples), and students (an ordinary control group used in many experiments, in psychology and economics). Nese et al. set out to test three things:

First, to test whether Camorra participants have a greater tendency to cooperate in the Prisoners’ Dilemma game than ordinary criminals or students. Second, to test whether Camorra members differ from members of the other two groups in their reaction to the presence of external sanctions, and third, when the possibility of third party punishment is introduced, to analyse how the application of sanctions by members of the different groups under study varies.

Their sample is made up of 109 students from the University of Campania-Luigi Vanvitelli, 129 Camorra from Secondigliano jail in Naples, and 109 ordinary criminals from another prison in the same province as the university. Nese et al. explain the experiment as follows:

The experiment comprised two different designs: a one-shot Prisoners’ Dilemma (PD) and a one-shot Prisoners dilemma with third party punishment (PD-TPP)... In the PD design, at the beginning of the sessions, each subject was provided with an envelope that was labelled A or B and a number that identified the subject... A (B) subjects were endowed with 10 tokens and were paired with B (A) subjects. The (A and B) subjects had to (simultaneously) determine whether to keep the tokens or send them to the partner. If subjects sent the tokens to their (anonymous) partner, the researcher would triple the amount. Thus, the game had four possible outcomes: (10, 10), (40, 0), (0, 40), (30, 30).

So, this is a classic prisoners' dilemma, because both players have a dominant strategy to keep the tokens. If you doubt this, skip ahead to the end of this post [*], where I show the Nash equilibrium for this game (but make sure you come back to here afterwards!). Continuing with the explanation of the experiment:

The PD-TPP had a two-stage design involving three types of subject (A, B and C). The first stage corresponded to the PD and our procedures were precisely the same; the fundamental difference being that A and B were aware that the C player could intervene at the second stage and could thus influence their final payoff by awarding deduction points to one (or both) of them. In fact, at the beginning of the second stage, after A and B had determined whether or not to send the tokens, player C was endowed with 40 tokens and had to decide whether to keep the tokens or spend some or all of their endowment so as to deduct points from A and/or B. One deduction point would decrease A and B’s total payoff by three tokens... Thus, C was asked to indicate on the decision sheet how many deduction points he would allocate for each of the four possible outcomes in the PD: (CC), (DD), (CD), (DC).

In the outcomes in that last sentence, C refers to 'cooperate' (send the tokens), and D refers to 'defect' (keep the tokens). Nese et al. ran this experiment with the students, and each group of prisoners, separately - that is, there is no mixing between the groups. Their key results are summarised in Figure 1 in the paper:

In the ordinary prisoners' dilemma, students cooperate significantly more than ordinary criminals. However, Camorristi cooperate significantly more than either of the other two groups. Introducing the possibility of punishment increases cooperation among ordinary criminals, but decreases cooperation among students and Camorristi. In terms of punishment behaviour, Nese et al. found that:

...all three groups punished defectors in roughly equal measure when their co-respondent also defected. Camorra inmates punished defectors - when their counterpart co-operated - significantly more and more often than the other two groups... In contrast to students, both types of prisoner sometimes punish co-operators as well as defectors; the tendency being slightly more pronounced amongst ordinary criminals than Camorristi.

Nese et al. then take things a bit further, looking at how the results vary for participants who have different levels of cooperativeness, reciprocity, and locus of control (all measured by a survey). They find that:

...(a) across the three different samples, rather unsurprisingly, the main driver of pro-social behaviour, is a cooperative attitude; and, (b) perhaps more significantly, the greater tendency towards co-operation shown by Camorristi compared to either students or ordinary criminals remains statistically significant, even controlling for individual attitudes towards co-operation.

And in terms of punishment behaviour:

Controlling for individual preferences... a more co-operative attitude and a stronger internal locus of control negatively affect the size of punishment whilst being a reciprocator tends to increase it...

Introducing terms for individual preferences towards cooperation, reciprocity and locus of control, it emerges that amongst Camorristi the tendency to punish increases with the belief in the appropriateness of reciprocity –particularly positive reciprocity –and with a more internal locus of control (regarding good events), but falls as the tendency towards co-operation increases. Again, for ordinary criminals, the sign of the effects is typically reversed: subjects with a strong internal locus are less likely to punish, as are (especially positive) reciprocators whilst those who are more oriented towards co-operation punish more.

Taking these results all together, Nese et al. conclude that:

Camorristi inmates demonstrate a high degree of cooperativeness and a strong tendency to punish defectors. Moreover, the attachment to co-operative (in-group) norms of behaviour amongst Camorristi is completely reversed when such norms are externally imposed –leading to a significant reduction in co-operation once an external ‘judge’ is introduced.

This behaviour is quite different from that observed amongst ordinary criminals who are less willing to co-operate with each other than either students or Camorristi in the absence of a referee, but who become more co-operative under the threat of externally imposed punishment. The behaviour of ordinary criminals suggests an element of opportunism which is entirely lacking - or perhaps more accurately - completely overwhelmed by the more honour-bound mores of the Camorra, with its emphasis on the negative nature of betrayal and the rejection of external authority, accompanied by the threat of severe sanctioning of within-group rule breakers.

Interesting. I wonder what sort of results we would get for gang members in New Zealand?

[HT: Marginal Revolution, back in January]

*****

[*] The game is outlined in the payoff table below.

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If B chooses to keep the tokens, A's best response is to keep the tokens (since 10 is a better payoff than 0) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If B chooses to send the tokens, A's best response is to keep the tokens (since 40 is a better payoff than 30);
3. If A chooses to keep the tokens, B's best response is to keep the tokens (since 10 is a better payoff than 0); and
4. If the Police chooses to send the tokens, B's best response is to keep the tokens (since 40 is a better payoff than 30).

Note that A's best response is always to choose to keep the tokens. This is their dominant strategy. Likewise, B's best response is always to choose to keep the tokens, which makes it their dominant strategy as well. The single Nash equilibrium occurs where both players are playing a best response (where there are two ticks), which is where both A and B choose to keep the tokens. Notice that by both playing their dominant strategy and keeping the tokens, both players are worse off than they would be if they had both sent the tokens. This is a prisoners' dilemma game because, when both players act in their own best interests, both are made worse off.