Christopher X J. Jensen
Associate Professor, Pratt Institute

Rand and Nowak paper on antisocial punishment in public goods games

Posted 19 Aug 2011 / 2

Researchers who study cooperation cannot agree on the role that punishment plays in maintaining the widespread social cooperation observed in nature and human societies. As is true in any scientific discipline, the social experiences of scientists studying cooperation influence their hypotheses. And looking at the societies that we live in, it is easy to see how opposing hypotheses regarding punishment could emerge. On one hand, we live in societies in which there is or appears to be a lot of punishment: societies invest large amounts of effort in maintaining large police forces, judicial systems, and prisons. On the other hand, we do not seem to engage in very much direct punishment of each other on a daily basis: in fact, the absence of “vigilante justice” is one of the hallmarks of a stable society. So what role did punishment play in the evolution of cooperation?

Experimental work has provided equivocal evidence in regards to the role of punishment in fostering cooperation. While some people are willing to incur costs in order to punish defectors in experimental public goods games, defectors are also perfectly willing to punish cooperators in retaliation (when given the opportunity by the rules of the game). This sort of retributive punishment is called “antisocial” because it destabilizes contributions to the common good. Game theorists have had a difficult enough time explaining prosocial behaviors that do not match their definition of rationality; if they cannot explain prosocial behavior, how do they explain antisocial behavior? If a lot of human generosity cannot be explained through a simplistic depiction of “rationality”, think about how difficult it is to understand the rationale for punishing behavior on the part of non-cooperators.

Martin A. Nowak is in the camp that believes that so-called “altruistic punishment” is not an important mechanism for maintaining cooperation. As theoretical games are his framework for explaining the evolution of cooperation, it should come as no surprise that he uses game theory to show that punishment does not encourage cooperation. In a recent paper co-authored with David G. Rand entitled “The Evolution of Antisocial Punishment in Optional Public Goods Games” (published in Nature Communications), Nowak uses a simple public goods game to tease out the role that punishment can play in this idealized social system. As is common in the work of Nowak, the selective process modeled is not meant to specifically depict either genes or culture: it could work for either form of evolution.

The game construct that they use creates a rock-paper-scissors dynamic with three possible player strategies: defector, cooperator, and loner. The loner strategy avoids getting involved in the public goods game, neither donating to nor capitalizing from public donations. As is the case for other public goods games, defectors can undermine cooperators in the absence of punishment. But the addition of the loner strategy allows cooperators to invade loners and loners to invade defectors. Thus, the game has no optimal strategy and instead will cycle between strategies as frequency-dependent selection continually purges the numerically-dominant strategy.

Adding punishment to this three-strategy system creates an interesting new dynamic. As has been shown by previous studies, if cooperators are the only ones allowed to punish, they can effectively resist invasion by the other two strategies. Thus, under very restrictive conditions so-called “altruistic punishment” can be effective.  But what Rand and Nowak show is that this effect of punishment is really just an epi-phenomenon of the overall effect that punishment can have on the system. When they allow all three strategies to exercise the punishment option, what they find is that all strategies use punishment to avoid invasion by the strategy to which they were previously vulnerable. While cooperators can punish defectors, defectors can also punish loners (who are presumably a threat because they do not participate in the public goods game) and loners can punish cooperators (who are a threat because they realize higher returns through cooperation than the isolated loners). As such, the loners are engaging in antisocial punishment because they punish behavior that contributes to the common good; but this “common good” is really only a common good for those who play the public goods game, and because loners opt out of the game they do not enjoy this common good.

Based on these findings, Rand and Nowak suggest that punishment is not really a mechanism by which cooperation is maintained, but rather just a mechanism by which particular strategies can compete with strategies to which they are vulnerable. While allowing exclusive punishment delivered by cooperators increases the level of cooperation the system, when all strategies are  capable of punishment, levels of cooperation decrease to the levels seen when no punishment of any kind was allowed. The take-home message is that unless punishment can be made the exclusive privilege of cooperators alone, punishment does nothing to encourage cooperation: in fact, it is better depicted as a mechanism for competition.

Perhaps what makes this paper most interesting is that it is not a purely theoretical paper: the authors also conducted a small experimental study which presented  human participants with the opportunity to assume any of the three roles depicted in the model. Based on this small experiment, it does appear that so-called loners – individuals who opt out of optional games – are more likely to engage in antisocial punishment than cooperators or defectors. In a way, this makes some sense: loners are in general threatened by larger groups and the possible power they will wield, so punishing members of these groups is a way of disrupting the power of groups. Sounds like Theodore Kaczynski to me!

So if antisocial punishment is neither rationally explainable nor effective at fostering cooperation, why is this particular game theory analysis at all important? From what I can tell, Rand and Nowak really want to show that internal group cycles of punishment will lead to the implosion of that group (or at least its instability). This suggests that internal group behavior alone cannot explain the maintenance of cooperation: there needs to be significant competition between groups (in other words, group selection) in order for punishment as a strategy to be purged from the population.

I also think that it is important to notice that while the Rand and Nowak paper suggests that conventional game theory does not support punishment as a mechanism for maintaining cooperation, that does not mean that punishment  has not played an important role in the evolution of cooperation.  First of all,  punishment may be reserved not for other group members, but for the members of rival groups (Bingham 1999, 2000). Second of all, we should always keep in mind that proving that punishment is theoretically impossible only suggests that punishment cannot exist in the world depicted by the theory. What if the world that we actually live in is not well-depicted by these simple game theory constructions? It seems to me that all that this latest paper on punishments shows is that current theory cannot account for empirical observations.

Altruism, Articles, Cooperation, Game Theory, Punishment

2 Comments to "Rand and Nowak paper on antisocial punishment in public goods games"

Julián García 24th June 2012 at 6:37 pm

It is worth noticing that in some cases cooperation can beat both, antisocial punishment and cooperation. This depends on how loners interact with others. The paper by Rand and Nowak only explores one possibility, but if loners are excluded from punishment altruistic punishment still prevails:

Chris Jensen 28th June 2012 at 4:49 pm

Thanks for pointing out your paper Julián. I read it and reviewed it here.

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