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If the cost and effectiveness of punishment does not affect the overall levels of extraction observed in CPR games, we would expect to find no difference between treatments, provided the incentives for cooperation and defection remained the same across economic environments. In our treatments, marked differences were found in the average levels of extraction at each different punishment effectiveness ratio. Differences also occurred in the degree of extraction over time. Higher punishment effectiveness ratios produced much more constant levels of extraction over time.

Result one: Stronger punishment results in lower extraction levels

We find significantly lower extraction levels associated with higher punishment ratios. This decrease in extraction is modest but statistically significant and monotonic. All punishment treatments had significantly lower extraction levels than those with no punishment, with stronger punishment showing a more significant difference (first row of table 11). Though a ratio of 1:5 was not significantly different to a ratio of 1:3 (p=0.447), a ratio of 1:9 achieved lower contributions compared to all other treatments (as shown in the right-hand column of table 11). Figure 5 shows the extraction results over time. Note the stacked lines created by the increasing effectiveness of punishment in reducing extraction from the low payoff CPR environment. Despite the significant improvement with stronger punishment, extraction levels were still considerably higher than the social optimum of 5, with the lowest mean contribution achieved being 6.86 with

a punishment ratio of 1:9 (table 10) in the low payoff environment. Behaviour was less responsive to increased punishment strength compared to results in the linear VCM (Nikiforakis & Normann, 2008).

Table 10: Mean extraction levels

Standard errors are in parentheses. P-values for Wilcoxon signed-rank tests of difference in public contribution levels between the first and last five periods are in the right column.

Treatment Periods 1-10 Periods 1-5 Periods 6-10 Wilcoxon signed-rank p- value No punishment 7.59 (2.60) 7.45 (2.78) 7.73 (2.42) 0.706 1:3 punishment 7.26 (2.60) 7.13 (2.64) 7.40 (2.57) 0.097 1:5 punishment 7.19 (2.46) 7.10 (2.56) 7.28 (2.35) 0.637 1:9 punishment 6.86 (2.56) 6.86 (2.60) 6.87 (2.51) 0.549 1:9 punishment high payoffs 8.81 (2.72) 8.29 (2.74) 9.33 (2.61) 0.001

Table 11: Differences in extraction between treatments

P-values are for Mann-Whitney tests (2-tailed) of difference in extraction levels between punishment treatments.

1:3 punishment 1:5 punishment 1:9 punishment

No punishment 0.052 0.006 <0.001

1:3 punishment . 0.447 0.001

Figure 5: Mean extraction - low payoff treatments

Result two: Stronger punishment inhibits decline in cooperation over time

Although average extraction remained lower in the treatments with punishment than those with no punishment, several of our treatments were characterised by a decline in cooperation over time, with higher extraction in the later periods. This outcome was particularly marked in the high payoff treatment (see tables 10 and 12 and figures 6 and 7). Spearman correlations in table 12 indicate significant declines for both the 1:3 punishment treatments and the 1:9 high payoff treatments.

Declines were not significant for the no punishment, 1:5 and 1:9 ratio treatments. In the case of the no punishment treatment, this is likely to be due to the fact that extraction quickly reached a higher level than in the other treatments, remaining relatively flat but close to the Nash equilibrium. In the case of the 1:5 ratio treatment, decline appears to be somewhat curbed by punishment. Extraction in the 1:9 punishment treatment was particularly flat with a Spearman correlation coefficient of -0.003 and a p-value of 0.952, as shown in table 12. Table 10 also compares the mean extraction levels from the first and last five periods, including Wilcoxon signed-rank tests for significance of differences between early and late periods. Figure 6 illustrates this information, showing the especially marked decline in the higher payoff environment.

Table 12: Correlations in extraction over time

P-values for Spearman correlations (2-tailed) across all 10 periods

Treatment Spearman p-value

No punishment 0.215

1:3 punishment ratio 0.008

1:5 punishment ratio 0.319

1:9 punishment ratio 0.952

Figure 7: Mean contributions - low payoff treatments

4.3 Punishment – use

Result three: More effective punishment and higher incomes generate greater demand for punishment (punishment is a normal good)

In all cases, higher punishment effectiveness induced greater use of punishment, with significantly greater levels of punishment observed in stronger punishment treatments. This is evident in figure 8, with significance established in table 14. In effect, increasing the punishment ratio reduces the cost of a given amount of deduction, which generates increased demand. This finding is consistent with previous findings in relation to punishment as a normal good; for example, Ostrom et al. (1992) and Nikiforakis & Normann (2008). In addition to the impact of reduced cost, increased income (as observed in the high payoff treatment) had a further effect of increased demand for punishment.

The observed level of punishment over time differed markedly between treatments (tables 13 and 14). For the 1:3 punishment ratio, a relatively low level of punishment occurred and was constant over time. Increasing this ratio to 1:5

0 1 2 3 4 5 6 7 8 9 10 M ea n ex tr ac tion Treatment Periods 1-5 Periods 6-10

produced initially high levels of punishment, but a decline in use over time. Given that this decline in punishment is not associated with a significant increase in extraction for this treatment, the implications for efficiency are positive (and indeed evident in the significant increase in efficiency over time in table 17). The declining level of punishment in the 1:5 treatment contrasts with the relatively constant level of punishment observed in the 1:9 treatment. Efficiency in the 1:5 treatment began lower than in the 1:9 treatment due to higher extraction levels, but was not significantly different in the latter periods (as shown in table 18) due to the decline in punishment costs.

Table 13: Mean payoff reductions received

Standard errors are in parentheses. P-values for 2-tailed Wilcoxon signed-rank tests of difference in between the first and last five periods are in the right hand column.

Treatment Periods 1-10 Periods 1-5 Periods 6-10 Wilcoxon signed-rank p- value 1:3 punishment 4.40 (5.89) 4.79 (5.70) 4.01 (5.89) 0.229 1:5 punishment 9.81 (11.94) 12.25 (12.63) 7.36 (10.69) <0.001 1:9 punishment 10.94 (16.93) 10.07 (15.87) 11.80 (17.91) 0.342 1:9 high payoff 17.89 (20.55) 15.56 (17.84) 20.21 (22.75) 0.052

Higher incomes in the high payoff treatment significantly increased the amount of punishment participants were willing to pay for. However, the quantity of punishment demanded increased less than the associated increase in income, in the high payoff treatment. Accordingly, the income elasticity of demand was relatively low at 0.66.

By contrast, demand was highly-responsive to price for the initial drop in cost from a 1:3 to a 1:5 punishment ratio. Price elasticity appears to fall rapidly above this level, however, as shown by the demand curve in figure 9. It seems likely that the quantity of punishment demanded would continue to increase as the

punishment ratio increases further, up to some maximum, but this is an open empirical question left for further research.

Figure 8: Payoff reductions received in each period

Figure 9: Demand for punishment at 1:3, 1:5 and 1:9 effectiveness ratios

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 50 100 150 Price per unit of punishment

Table 14: Differences in punishment use

P-values for Mann-Whitney tests (2-tailed) of difference in punishment levels between treatments.

Periods 1-10

1:5 punishment 1:9 punishment 1:9 punishment high payoff

1:3 punishment <0.001 <0.001 <0.001

1:5 punishment . 0.044 <0.001

1:9 punishment . . <0.001

Periods 1-5

1:5 punishment 1:9 punishment 1:9 punishment high payoff

1:3 punishment <0.001 0.111 <0.001

1:5 punishment . <0.001 0.519

1:9 punishment . . <0.001

Periods 6-10

1:5 punishment 1:9 punishment 1:9 punishment high payoff

1:3 punishment 0.035 <0.001 <0.001

1:5 punishment . 0.135 <0.001

1:9 punishment . <0.001

Result four: More effective punishment is used to increasingly target defectors

The distribution of punishment points that were assigned demonstrated a clear pattern of targeting defectors, as shown in figure 10. Because the social optimum (and average contribution) is at a level of extraction above the minimum but below the maximum, we also observe punishment being assigned to those contributing less than the group average. While it is tempting to attribute this result to group norm enforcement, such a claim cannot be made definitively. For example, a number of participants used strategies of maximum extraction (all 12 tokens) coupled with assigning the maximum number of punishment points to every other participant, in order to enforce asymmetrical extraction levels within

the group. While the strategy is certainly not random, it could not be described as enforcing a shared norm. Further information is required regarding participants’ attitudes to norms and punishment to decouple these possible explanations.

Figure 10: Payoff reductions received