2. Experiments with Human Subjects: Results and Discussion

Figure 1 A–C shows average contribution levels in the three treatments, average punishment intensity in the punishment and sanction treatments, and average punishment frequency in the same two treatments. During rounds 1–10 contribution levels decline in all treatments, with average contributions being 8.33, 6.25 and 8.23 in the message, the punishment and the sanction treatment respectively; the Kruskal-Wallis test does not find any differences between the three data-sets (p = 0.1821). For rounds 16–20, average contribution levels contribution levels are 9.90, 10.65 and 14.46 in the message, the punishment and the sanction treatment respectively. This implies that contributions in the sanction treatment are significantly higher by 36% than in the punishment treatment and significantly higher by 52% than in the message treatment; in this case the Kruskall-Wallis test finds significant differences between the three treatments (p = 0.07). In the last ten rounds, when punishment and normative message opportunities are switched off, contributions decay in all three cases to average levels of 5.05, 3.75 and 9.08 in the message, the punishment and the sanction treatment respectively. Now cooperation levels in the sanction treatment exceed by 142% those obtained in the punishment treatment and by 79% those in the message treatment, with the Kruskal-Wallis test finding a significant difference (p = 0.04). Overall, the contribution levels are quite low with respect to those reported in [6], [16], where the same parameter values are used. An experiment comparing contribution behaviour in student populations in Spain, the Netherlands, the US and Japan (see [27]) finds that contributions in Spain (Pompeu Fabra University) are the lowest, although the difference is not statistically different.

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larger image TIFF original image Download: Figure 1. (A–C) Results of the Experiments with Human Subjects. Panel A depicts the contribution levels obtained in the human experiments. Panel B depicts the punishment intensity observed in the human experiments. Mean punishment intensity is defined as the average number of punishment units sent, whenever punishment is used, i.e. all instances of zero punishment are excluded. Panel C depicts the punishment frequency observed in the human experiments. Punishment frequency measures the average number of times punishment is used, regardless of the number of punishment units sent. https://doi.org/10.1371/journal.pone.0064941.g001

Using the Mann-Whitney test, the difference between average contributions in the sanction and the punishment treatments in rounds 11–20 is significant (p = .048). There is no significant difference in contributions between sanction and message for rounds 11–15 (p = .7290), but contributions are significantly higher in sanction than in message for rounds 16–20 (p = .0179). Average contributions are significantly higher in the message than in the punishment treatment (p = .0833) in rounds 11–15, but no difference in rounds 16–20 (p = .2987).

The average number of punishment points sent is 1.73 times higher in the punishment than in the sanction treatment (see also Table S1 and Figure S5 included in the Supporting Information). Using the Mann-Whitney test, we find that average punishment points allocated per member is significantly higher in the punishment than in the sanction treatment (p = .0005) (1.24167 vs. 0.1625 average points sent). Moreover, in the punishment treatment, the frequency of punishment is 5.68 times higher than in the sanction treatment. Using the Mann-Whitney test, we find that in the punishment treatment, the frequency of punishment is significantly higher than in the sanction treatment (p = .0004). Figure S4 in the Supporting Information shows mean punishment as a function of the punished subject’s contribution minus that of the punisher for the two treatments involving punishment. Table S3 in the Supporting Information provides support for the idea that those players who contribute less than asked to are strongly punished.

Due to higher contributions and lower punishment, average net earnings are 31% higher in the sanction than in the punishment treatment for rounds 11–20 and 16% higher than in the message treatment for rounds 16–20. Unlike in the other two treatments, earnings in the sanction treatment are 12.38% higher in rounds 11–20 than in rounds 1–10 (see also [14], [24]). By using sanction, the gains from higher contributions are not offset by the associated punishment costs. Payoffs are higher in the sanction than in the punishment treatment for rounds 11–15 (p = .0010) and for rounds 16–20 (p = .0055). Payoff levels are not higher in the message than in the sanction treatments for rounds 11–15 (p = .8174), but are significantly higher in sanction than in message for rounds 16–20 (p = .0242). Payoffs are significantly higher in the message than in the punishment treatment (p = .0007) in rounds 11–15, but no difference in rounds 16–20 (p = .4529).

We can use the within-subjects nature of our design to compare contribution levels in the second block with those of the first block. A Wilcoxon test finds that, unlike in the other two treatments, in the sanction treatment payoffs are significantly higher in rounds 11–20 than in rounds 1–10 (p = .0096) and than in rounds 21–30 (p = .0022). This is in contrast to the results reported in [6]–[7], [18].

In both the message and sanction treatments, messages from peers help subjects soon to identify the prescribed amount of contribution and to form expectations about the consequences of violations. In both treatments, subjects’ expectations and their behaviours rapidly converge. Figures S1 and S2 in the Supporting Information show that the percentages of individuals that sent a message and the average required contribution levels in rounds 11–20 are quite similar for the two relevant treatments. Table S2 in the Supporting Information shows that in both treatments subjects that ask for high contributions are those who contribute at high levels. Figure S3 in the Supporting Information shows that the use of the three different messages differs somewhat across the two relevant treatments. Specifically, behaviour in the sanction treatment exhibits a stronger concentration on message 1 (“In this way we are all better off”), while in the message treatment message frequencies are a little more dispersed.

The value added by material punishment to norm communication consists in strengthening the normative expectations, thus increasing the norm salience in subjects’ minds. As shown by the results in the message treatment (and differently from [14]), when norms are verbally transmitted but not enforced by material punishment compliance soon declines. Since a high number of participants deviates from the contribution due, the norm becomes less salient and inefficient in sustaining compliance. In the sanction treatment, subjects immediately meet the prescription and the possible use of punishment only sustains the contribution level reached. In contrast, in the punishment treatment, in which information about norms can only be inferred from the material cost received, the cooperation level reached is substantially lower and the costs for achieving it is higher than in the sanction treatment. When modelled only in material terms, punishment is scarcely effective in helping subjects to find out the norm. Far from coordinating, subjects separately preceed by trial and error.