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Game theory

How to treat those of ill repute

Nature volume 457, pages 3940 (01 January 2009) | Download Citation


A much-needed theoretical analysis deals with whether the principle known as 'costly punishment' helps to maintain cooperation in human society. It will prompt a fresh wave of experiments and theory.

Human societies are built on cooperation, especially on reciprocation1— I help you and you help me, or I help you and someone else helps me. In the first case, help is directly reciprocated by help. In the second, called indirect reciprocity, I gain a good reputation and so I can expect help when in need.

But how shall I treat someone with a bad reputation? Shall I just refuse help or shall I punish this person at a cost to myself? Costly punishment can enhance cooperation2,3 in experiments with human subjects, but potentially with no net benefit4: the costs of punishment usually, although not always5, neutralize gains from enhanced cooperation. On page 79 of this issue, Ohtsuki et al.6 describe a theoretical test of whether either refusing help to or punishing someone with a bad reputation might lead to a cooperative society. They conclude that, except under certain rare conditions, punishment does not produce that outcome.

When you meet someone needing help, you can help (cooperate), refuse to help (defect) or not only refuse to help but, in addition, decrease the needy person's wealth (punish). Both cooperation and punishment are costly for you, but respectively create a larger benefit or larger loss for the person needing help. Defection is cost neutral.

How you behave depends on the reputation — good or bad — of the needy person, and depends upon your 'action rule'. An example is 'cooperate with someone with a good reputation and defect with someone with a bad reputation' (CD). The reputation you yourself gain by applying your action rule depends on the social norm of your society. Under the norm 'stern-judging', for example, you gain a good reputation when cooperating with good or when defecting with bad, and a bad reputation in all other cases. Thus CD always leads to a good reputation under stern-judging.

Another action rule, CP, prescribes 'cooperate with good and punish bad'. Under stern-judging, with CP you will achieve a good reputation when you interact with someone with a good reputation and a bad reputation when you interact with someone with a bad reputation. But under a different social norm, 'shunning' (cooperation with good or punishment of bad leads to a good reputation), CP will always provide you with a good reputation (Fig. 1).

Figure 1: Action rules, social norms and the story of Alice and Bob.
Figure 1

Bob meets Alice and learns whether Alice has a good or a bad reputation. On the basis of that, Bob may either help (cooperate), refuse help (defect) or refuse help and, in addition, decrease Alice's wealth (punish). How Bob reacts is specified in his action rule. Bob's own reputation depends on how society's social norm evaluates Bob's reaction to Alice's reputation. The social norm 'stern-judging' evaluates cooperation with good as good and punishment of bad as bad; the social norm 'shunning' evaluates cooperation with good as good and punishment of bad as good. Each social norm specifies which reputation to assign for each of the 6 possible scenarios (3 actions of Bob for 2 reputations of Alice). This leads to 26 = 64 social norms.

In their simplest model, Ohtsuki et al.6 assume that everybody has the same opinion of the reputation of another person or has the same level of fallibility in assigning an incorrect reputation. For such a society, they test for each of the 64 different social norms (Fig. 1) whether an action rule exists that both generates a cooperative society and is evolutionarily stable — meaning one that resists replacement (invasion) by any of the other eight possible action rules (Fig. 1).

Ohtsuki et al. find that the two action rules that induce cooperation and resist invasion are those described above — CD under stern-judging and CP under shunning. Nonetheless, the average pay-off is lower if the action rule uses costly punishment, while the stability conditions are less restrictive.

However, which parameters determine which rule is most efficient in the sense of leading to the highest average pay-off at equilibrium? It turns out that a crucial one is the accuracy of assigning the correct reputation to everybody. If this accuracy is too low then only a DD action rule is efficient, under which nobody cooperates. If the accuracy is high enough, then CD can be efficient. For intermediate values of the accuracy, there is a small window in which CP can be efficient, as reflected in the title of the paper6: “Indirect reciprocity provides only a narrow margin of efficiency for costly punishment.”

In a further step in their modelling, Ohtsuki et al.6 dropped the assumption that all good or bad reputations are publicly known, and allowed individual knowledge of reputations. They found that the stability of both CD and CP is lost when there is the smallest error in distinguishing between good and bad. When individuals start to communicate with each other and adjust their assessments of everybody's reputation, the CP action rule can be stably maintained. Then, when reputations become even more publicly agreed upon through more efficient gossip, both CD and CP are stably maintained under their corresponding social norms. Experimental studies7 in indirect reciprocity have shown that gossip can indeed serve as a surrogate for direct observation. But it will take further empirical research to find out whether gossip is efficient enough to re-establish both CD and CP.

The next question addressed by Ohtsuki et al. was which kind of society someone might prefer to live in. To this end, they simulated one society with CD under stern-judging and another with CP under shunning. When individuals can choose freely between them, the CD society — that with the higher expected pay-off — is preferred. Thus, the CP rule loses to CD when people can choose between societies with different norms.

This last result can be compared with our own experimental work with human subjects8. We found that when individuals had the choice between a CD-only society and one with both CD and CP, they ultimately preferred the latter. Compared with a CP-only control, punishing acts were largely reduced in the CD plus CP society but were concentrated on the most uncooperative players, rendering them more cooperative. Our experimental societies in which CD and CP coexisted were more efficient than those with only CP, suggesting that they have a more complex action rule: respond to good with cooperate, to bad with defect, and to very bad with punish. Such a possibility sets a challenge for theorists.

Finally, given that Ohtsuki et al. show that the social norm of a society determines which action will prevail, another task is to uncover the social norms of real societies and analyse which action rule to expect. Ohtsuki et al. assume that all social norms are equally likely. However, the more information a norm requires in order to develop, the more susceptible it is to errors and the more costly is the information acquisition9. Such restrictions may challenge any social norm that otherwise dominates: for example, in an experimental study10, the subjects had a majority social norm similar to shunning that was 'low observation' and 'memory demanding'.

Ultimately, study of the joint evolution of social norms and action rules under natural constraints is the goal for the future. Ohtsuki et al. have prepared the ground for that endeavour.


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  1. Bettina Rockenbach is in the Department of Economics, University of Erfurt, Nordhäuser Straße 63, D-99089 Erfurt, Germany.

    • Bettina Rockenbach
  2. Manfred Milinski is in the Department of Evolutionary Ecology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Straße 2, D-24306 Plön, Germany.

    • Manfred Milinski


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