Inequality and Peer Punishment in a Common-Pool Resource Experiment

Institutions like communication, voting, and peer punishment can enable self-governance in common-pool resources (CPRs) when users have equal capacities (i.e., endowments) to extract the resource (Cason and Gangadharan, 2015; Ostrom, 1990, 2006).¹ But in many cases users have unequal endowments (e.g., some users have more nets to cast into a fishery). Andersson and Agrawal (2011) examine more than two-hundred CPR case studies across three continents to study the effects of variation in endowments (wealth) on conservation. They find that inequality and conservation are negatively associated where institutions are weak or non-existent.² This suggests that institutions moderate the effects of inequality.

What is unclear is whether inequality directly impacts the effectiveness of institutions. Controlled lab experiments can help clarify the relationship between inequality and institutional effectiveness by holding the institution constant and varying inequality (Ostrom, 2006). Experiments find mixed evidence on the effect of endowment heterogeneity on voting (Margreiter et al., 2005) and communication (Cardenas, 2003; Hackett et al., 1994). But little is known about the interaction between inequality and punishment in CPRs.³ We fill this gap in the literature.

Our experiment is based on the homogeneous endowment CPR game by Kingsley (2015) and similar to the nonlinear public goods game with heterogeneous endowments and punishment by Kingsley (2016). Subjects were grouped into fours and played fifteen periods of a CPR game. We have 2 × 2 treatments: {Equal, Unequal} × {No Punishment, Punishment}. In our Equal treatments, each subject was given an endowment of 50 experimental dollars (EDs). In our Unequal treatments, two subjects were given endowments of 40 EDs (Low) and two subjects were given 60 EDs (High). The distribution of endowments was random and fixed across periods. We then vary whether subjects could peer punish using the standard 1:3 punishment technology (in which subjects pay one ED to punish a target three EDs). Like Kingsley (2016), during the punishment stage subjects could observe extractions from the CPR but not individual endowments.

Groups that self-govern a commons must agree on (1) the total level of extraction and (2) how that total is divided among group members (Ostrom, 2006). Inequality in our design does not change the solution to the first problem: the aggregate social optimum is the same across treatments. Instead, inequality introduces three normatively appealing ways groups can achieve the social optimum (i.e., solve the second problem): Equal Extractions, Equal Proportions, and Equal Earnings (Cappelen et al., 2007; Kingsley, 2016; Nikiforakis et al., 2012; Reuben and Riedl, 2013). In Equal each of these extraction norms coincides with the symmetric social optimum. However, in Unequal each norm dictates a different pattern of extractions and, importantly, a different distribution of the socially optimal group earnings. This is important because peer punishment is most effective when groups agree on a norm (and thus agree on which extractions should be punished). So, if groups with inequality struggle to agree on a division of the social optimum, it is possible that peer punishment will be less effective.

We find that peer punishment is, in fact, more effective in Unequal than Equal. In the absence of punishment there is no difference in earnings across treatments. However, when punishment is introduced, and after accounting for the costs of punishment, groups in Equal earn less across all periods, whereas groups in Unequal earn a similar amount relative to their no punishment counterparts. In later periods, earnings are significantly higher in Unequal with punishment relative to Equal. This is particularly interesting because average extractions across the punishment treatments are indistinguishable.

However, treatment effects are not limited to central tendency. For example, De Geest and Stranlund (2019) show that coordination in social dilemmas like CPR games can be measured by testing differences in behavioral variance across treatments. We show that an important effect of punishment in Unequal was on the variation in extractions. Using the variation test introduced by De Geest and Stranlund (2019) we find that punishment reduced the variation in extractions in Unequal (for both Low and High) but not in Equal. In other words, punishment appeared to induce more coordinated behavior in Unequal than Equal.

Evidence of better coordination in Unequal also bears out in how subjects used punishment. To get a more detailed look at enforcement across treatments we calculate the expected cost of punishment — the probability of punishment times the magnitude of punishment — for each possible extraction. While unconditional average punishment is similar across treatments, the conditional expected costs of punishment were higher in Equal than Unequal, stemming from a significantly higher probability of punishment in Equal. Taken together, our results point to a greater degree of coordination and agreement on the appropriate level of extractions in Unequal, resulting in less punishment and higher earnings.

Our main contribution to the CPR literature is to show that inequality can make peer punishment more effective. One plausible explanation is that inequality created a focal point in the choice space, making it easier for groups to coordinate on and enforce an acceptable division of total extractions.⁴ Our results show that Low types coordinated around the Equal Earnings norm, and in response, High types matched. This coordinate-and-match dynamic appeared when there was no punishment. Introducing punishment reinforced it: the variation of extractions by both types falls over time, and most telling, the distribution of extractions of Low pile up at the Equal Earnings norm. While this division of extractions was not optimal for Low types, the use of punishment indicates that it was acceptable. Punishment was mainly targeted at extractions that revealed High types, while extractions below the Low endowment were rarely targeted, likely to avoid misguided punishment, which can hinder the institution’s effectiveness (Nicklisch et al., 2016).

In Equal there was more punishment but less coordination. Cason and Gangadharan (2015) find similar results in a CPR with homogeneous endowments and argue that it is because of the inherent complexity of nonlinear strategic settings. CPR games like ours are nonlinear, meaning the social optimum and Nash equilibrium lie on the interior of the choice set, rather than on the boundaries (as they would in a linear game). As a result, it is harder for subjects to distinguish cooperative behavior and enforce it with punishment. Therefore, the salience of inequality may improve coordination by emphasizing the Equal Earnings norm as a focal point.

Of course, whether this holds true in other scenarios (e.g., more extreme inequality, self-governance with multiple institutions, and so on) is an open question. We discuss ways to improve our study and topics for future research in our conclusion.

We implement a 2 × 2 design in which we vary the distribution of endowments within groups (Equal or Unequal) and whether subjects have the opportunity to punish each other (No Punishment or Punishment). We use the same CPR and peer punishment design as De Geest and Stranlund (2019), Kingsley (2015), Kingsley and Liu (2014) and Apesteguia and Maier-Rigaud (2006), which is based on the canonical CPR model introduced by Ostrom et al. (1992). Payoffs to agent i in the absence of punishment are

where e_i is the agent’s endowment, g_i is the agent’s extraction from the CPR, w is the fixed return from the private account, n is the group size, $G=∑i=1ngi,andV(G)=aG−b(G)2$ is the production function of the CPR. The game is a social dilemma when a > w > b and 0 < b < 1.⁵ We assume that the parameters a and b, which determine the productivity of the CPR, are unaffected by agent decisions and regenerate with each new interaction between agents (and between subjects in the experiment). Setting w = 1, a = 6, b = 0.025, and n = 4 the socially optimal aggregate extraction G^S and the Nash equilibrium aggregate extraction G^N are

Our design uses a simple implementation of inequality. In each session, subjects were randomly assigned into groups of four and stayed in their groups for the duration of the experiment. Subjects within each group were then randomly assigned an endowment. In Equal, all subjects received the same endowment of 50 Experimental Dollars (EDs) at the start of each period. In Unequal, two subjects in each group received a low endowment (Low = 40), and the other two group members received a high endowment (High = 60). Note that the sum of endowments was identical across treatments $(∑i=1nei=200)$⁠. Subjects retained these endowments for the duration of the experiment. Subjects knew the distribution of endowments in their group, but they were never informed which group member had which endowment.

In our model (just like in Ostrom et al., 1992) the agent’s own endowment does not enter her best-response, and neither do the endowments of her group members. As a result, endowment heterogeneity does not affect the aggregate Nash equilibrium or social optimum, and thus does not affect group earnings at these points. However, groups can vary the distribution of these group earnings depending on the pattern of extractions across group members.

Table 1 shows extractions and earnings for the benchmarks in our design. First, we assume a symmetric Nash equilibrium where each group member extracts 40 EDs from the CPR. In this case each group member would earn 90 EDs in Equal and Low (High) members would earn 80 (100) EDs in Unequal each period.⁶

At the social optimum we consider three normatively appealing extraction norms: Equal Extractions, Equal Proportions, and Equal Earnings. As shown in Table 1, this distinction is irrelevant in Equal as each plausible norm dictates identical extractions and earnings across group members. However, in Unequal, each plausible extraction norm dictates a different distribution of group earnings. Under an Equal Extractions norm each group member extracts 25 EDs and Low members earn 102.5 EDs and High members earn 122.5 EDs. Under an Equal Proportions norm Low (High) members extract 20 (30) EDs and earn 90 (135) EDs each period. Finally, under an Equal Earnings norm Low (High) members extract 29 (21) EDs and earn 112.5 (112.5) EDs each period.

The experiment instructions displayed both individual and group payoff tables so that subjects could clearly discern the relationship between individual and group earnings (Kingsley and Liu, 2014). Furthermore, subjects were shown that extracting 100 EDs would maximize group earnings to ensure that, across treatments, subjects had the same understanding of the individual and group incentives.

Our experiment proceeded as follows. Subjects first decided how much of their endowment to allocate between two accounts: Account 1 (the group account) or Account 2 (the private account). After choosing extractions, subjects were shown their individual extraction, the group’s aggregate extraction, and their individual period earnings. In No Punishment, subjects would then continue to the next period.

In Punishment subjects would then proceed to the punishment stage. In the punishment stage, subjects chose how many deduction points to assign to each group member. Subjects in Equal and Unequal could observe each group member’s extraction by random ID, but they could not observe each group member’s endowment. Subjects in Unequal knew the distribution of endowments, but at no point in the experiment did they learn which group members had which endowments. We use the standard 1:3 punishment technology in which one punishment point assigned to an individual cost the sender 1 ED and the receiver 3 EDs. Subjects were constrained only by their initial payoffs when assigning punishment (and so payoffs in a period could be negative). Therefore payoffs in Punishment were

where $∑pij$ is the sum of punishment sent by i to all other group members j and $∑pji$ is the sum of punishment received by i from j at cost c = 3.

Subjects were recruited from the undergraduate population at the University of Massachusetts Amherst. Data was collected in Spring 2012 at the Cleve E. Willis Experimental Economics Laboratory. A total of eight sessions were conducted with a total of 120 subjects including eight groups in each of our four treatments. The average session lasted approximately one hour. Subjects earned an average of about $15.00, with a standard deviation of about $3.00.⁷

Taken together, our results show that punishment was more effective in Unequal than Equal.

We begin with earnings in Equal and Unequal. There are no differences in earnings across treatments without punishment. However, earnings with punishment are higher in Unequal than Equal. Within treatments, punishment reduced earnings in Equal, but had no overall effect on earnings in Unequal. Breaking down the effect by endowment we find that punishment increased earnings for Low types and decreased earnings for High types.

We then look at extractions and punishment. To see whether subjects in Equal and Unequal coalesced around one of the plausible extraction norms in Table 1, we consider ranksum and signrank tests of average group extractions, and changes in the variation of extractions over time.⁸ While average extractions with punishment are similar in Equal and Unequal, the variation in extractions was significantly lower in Unequal. Subjects in Unequal appear to coordinate-and-match around the Equal Earnings norm for Low types: the distribution of extractions by Low types centers at the norm, High types appear to match it, and introducing punishment tightened this coordinate-and-match dynamic. As a result, there was significantly less punishment in Unequal, and it was more effective at changing behavior.⁹

Table 2 shows average earnings across treatments for all 15 periods, early periods (Early, periods 1–7), and late periods (Late, periods 8–15). Comparing Equal and Unequal, there is no significant difference in earnings without punishment.¹⁰ But when punishment is introduced, earnings are significantly higher in Unequal in late periods.¹¹

The introduction of punishment significantly reduced earnings in Equal across all periods, although the difference is not significant in late periods.¹² By contrast, punishment had no effect on average earnings in Unequal.¹³ However, there was variation in earnings within endowment types. For Low types punishment significantly increases their earnings during the late periods.¹⁴High types earn significantly less overall, and the difference is driven by earnings in late periods.¹⁵

Table 3 shows average extractions in each treatment. Punishment significantly lowers extractions overall in Equal (z = 2.31, p = 0.02) and in Unequal (z = 3.36, p < 0.01), and in both treatments the effect starts early and gets more pronounced over time.¹⁶ When we break up the effect by endowment in Unequal, we find punishment significantly reduced extractions by High types (z = 2.94, p < 0.01) but not Low types (z = 0.26, p = 0.79).¹⁷

Figure 1 shows the distributions of extractions across treatments, endowments, and time (Early and Late). The first observation that stands out in the distributions is evidence of coordination-and-matching around the Equal Earnings norm in Unequal: Low types coordinated around it, and High types matched it. Extractions by Low (Panels B and E) with or without punishment are consistent with the Equal Earnings norm: signrank tests fail to reject the hypothesis that average group extractions by Low are different from 29 (No Punishment: z = 0.14, p = 0.89; Punishment: z = 0.07, p = 0.94).¹⁸ The effect is most striking in late periods with punishment. Panel E in Figure 1 shows extractions by Low piling up right on top of the Equal Earnings norm.

Turning to High types (Panels C and F), we can reject the hypothesis that their extractions adhere to any of the identified extraction norms.¹⁹ Instead, punishment leads High types to match extractions by Low types. Average extractions by High are significantly different from 29 in No Punishment (z = 2.38, p = 0.02), but they are not significantly different in Punishment (z = 0.70, p = 0.48).

Coordination in Unequal is also seen in the reduced variation in extractions. The standard deviations in Table 3 show that with punishment the variation in extractions decreased over time in Unequal but not Equal. Moreover, punishment clearly narrows the distributions of extractions in Figure 1 by both High and Low, particularly in late periods. To check for statistical significance we use χ² tests from a version of the modified Levene’s test of equal variances for clustered panel data introduced by De Geest and Stranlund (2019).²⁰ Since punishment needs time to take hold, we focus our tests on the later periods (i.e., we test for differences in variation in Panels D, E, and F in Figure 1).

Results from our tests confirm that punishment led to a significant reduction in variance in Unequal. The variation in extractions is significantly less among Low types (χ² = 31.74, p < 0.01) and High types (χ² = 4.58, p = 0.03) in late periods with punishment relative to no punishment. This suggests that introducing punishment tightened the coordinate-and-match dynamic we observe in Unequal.

By contrast, we find less evidence that subjects in Equal (Panels A and D in Figure 1) coalesced around the social optimum. While punishment significantly decreased extractions in Equal, there is still a large density of extractions above the social optimum. As a result, average group extractions with punishment were significantly greater than the symmetric social optimum (z = 2.38, p = 0.02), and there is no difference in the variation of extractions (χ² = 0.02, p = 0.89).

Now we look at how the use of punishment may have influenced coordination in Unequal and the lack thereof in Equal. Figure 2 shows counts of punishment in Panels A and B and average punishment in Panels C and D. Two points stand out.

First, subjects in Equal punished nearly twice as often as in Unequal (Panels A and B). There were 526 counts of punishment in Equal, or about a 40% unconditional probability of punishment; there were just 271 counts of punishment in Unequal (about a 20% unconditional probability of punishment). The difference between Equal and Unequal is significant (χ² = 8.37, p < 0.01).²¹ In addition, the unconditional probability of punishment was evenly spread between Low (125 cases) and High (146 cases), with no significant difference between them (χ² = 0.25, p = 0.62).

The second point that stands out from Figure 2 is that there was no difference in the magnitude of punishment across treatments. Panels C and D show average punishment for all positive instances (when punishment was greater than zero). While average punishment was larger in Equal than Unequal, the difference is not significant (z = 0.53, p = 0.60). Once again the difference between Low and High is not significant (z = 0.84, p = 0.40).

Next we turn to targeting. To understand how subjects targeted punishment at each other, we need to look at average punishment at different extractions. Moreover, punishment is clearly probabilistic, so we also need to look at the likelihood of punishment at different extractions. In other words, we need to look at expected punishment.

To estimate expected punishment we calculated the conditional probability of punishment times the conditional punishment size. We estimated the probability of punishment P (s > 0)_ijkt (s for sanction) from a probit regression and the punishment magnitude $𝔼[s|s>0]ijkt$ from a Poisson regression (since punishment data are count data). Our full specification is

where g_ikt is the extraction of subject i in group k and period t, g_jkt is the extraction of a target j, $g−ikt$ is the average extraction in group k in period t, $∑jnksijk,t−1$ is the total amount of punishment received by i in the previous period, period is the period t, µ_i(ν_i) are individual random effects, and $ϵikt(εikt)$ is the idiosyncratic error. Standard errors are clustered at the group level.

After estimating the parameters in Equation (4) we plugged them back in and calculated the derivatives for each possible extraction.²² For Equal the range was set to g_ikt ∈ [0, 50]. We split the estimation for Unequal in two parts: first when extractions pooled Low and High (g_ikt ∈ [0, 40]) and second when extractions revealed High (g_ikt ∈ [41, 60]). For each extraction in both treatments we calculated the predicted probability of punishment and the predicted magnitude of punishment. Multiplying each probability with the corresponding magnitude gave us the expected punishment from an average group member. Multiplying this number by 3 gave us the total expected punishment to a subject from their three group members.

Expected punishment is shown in Figure 3. In both treatments, higher extractions from the CPR were targeted with more punishment. However, expected punishments for extractions between [0, 40] were higher in Equal than Unequal. Reinforcing the results from Figure 2, the difference in expected punishment is driven by a higher conditional probability of punishment in Equal. In Equal, 35% of all extractions equal to or below 40 were punished. That number falls to 19% in Unequal.

In addition, Figure 3 shows both targeting and restraint in Unequal. Expected punishments in Unequal only ramp up at extractions of 40 and above. By definition, such extractions could only have come from High types. So when High revealed themselves, they were targeted with stiffer punishments. This created an incentive for High types to reduce their extractions to 40 or below.

At the same time, subjects in Unequal did not try to root out High types pooling among Low types. That is, we do not observe punishment targeted at extractions below 40 in the hopes of hitting a High type. In fact there was very little targeting of extractions around 21 (extractions by High if they complied with the Equal Earnings norm). This can be plausibly explained by subjects wanting to avoid mistakenly punishing Low types, since misguided punishment can lead to an unravelling of cooperation (Nicklisch et al., 2016).

Finally, we find that subjects were more responsive to punishment in Unequal. Like Cason and Gangadharan (2015) and Masclet et al. (2003) we estimate a linear model of changes in extractions in period t + 1 in response to punishment in t while controlling for the tendency for subjects to adjust their extractions to the group mean (the variable Deviation). We estimate separate models for extractions above and below the average group extraction in a given period while interacting treatment and endowment indicators with punishment received in t.

Our results are shown in Table 4. The coefficient to Deviation is negative and confirms the “regression to the mean” effect. Models (1) and (2) show that subjects who extracted below the group average reduced their extractions in the next round. The effect is consistent across endowments and treatments, and we find no significant difference between Equal and Unequal.

However, Model (3) provides further evidence that punishment was more effective in Unequal. Only in Unequal was punishment effective at reducing extractions when subjects extracted above the average, and we find a significant treatment effect. When we break down the effect of punishment by endowments in Model (4) we see that the effect in Unequal is driven by High types. This is likely due to the fact that High types were heavily targeted with punishment when they revealed their endowments, as shown in Figure 3.

Institutions moderate the effects of inequality in common-pool resource (CPR) management (Andersson and Agrawal, 2011). At the same time, experiments have shown that inequality can alter the effectiveness of institutions like communication (Cardenas, 2003; Hackett et al., 1994) and voting (Margreiter et al., 2005). In this paper we test how inequality in the form of heterogeneous endowments affects peer punishment in a CPR experiment.

Inequality splits the socially optimal level of extractions into three plausible norms around which groups could coordinate: Equal Extractions (subjects have the same extractions), Equal Proportions (subjects extract the same proportion of their endowments) and Equal Earnings (subjects have different extractions but the same earnings). We find that punishment reduced extractions in both our Equal and Unequal endowment treatments. However, punishment was more effective in Unequal. Low types appeared to coordinate around the Equal Earnings norm, High types matched the extractions of Low types, and punishment tightened this coordinate-and-match dynamic. The variation in extractions fell, punishment was sparse, and it was mostly targeted at High types who revealed their endowments. By contrast, there was more punishment in Equal, but it did not reduce the variation in extractions, and it did not change the behavior of subjects who tended to extract above the group average, leading to significantly lower payoffs. Taken together, our results suggest that inequality made punishment more effective and improved coordination within groups.

One plausible explanation for our results is that the Equal Earnings norm was a focal point around which Low types coordinated.²³ Indeed, there is a remarkable pileup of extractions by Low types right on top of the Equal Earnings level of extraction in the latter stages of the punishment treatment. While the salience of the Equal Earnings norm could be explained by inequity aversion (Fehr and Schmidt, 1999), it may also simply be because it was the social optimum norm at which Low payoffs were highest.²⁴ Either way, with subjects coordinating around this point, it was easier for subjects to distinguish and then target non-cooperation, thus making punishment more effective. This also explains why we see less punishment in Unequal, particularly on the extensive margin (the probability of punishment).

Despite the equivalence of the Equal Earnings norm across treatments, we observe less coordination, more punishment, and lower earnings in Equal. Cason and Gangadharan (2015) also document high social costs of punishment in a CPR game with homogeneous endowments. The authors attribute this to the fact that coordination is difficult in nonlinear strategic settings like CPR games because the social optimum and Nash equilibrium are on the interior rather than on the boundary of the choice set. Therefore, our study suggests that inequality may improve coordination by creating focal points which allow groups to better discern cooperative behavior.

The narrow takeaway from our study is that policy makers need to take into account inequality when designing and implementing incentive-based institutions (like peer enforcement) to manage CPRs. The general takeaway from our study — and many other studies, going back to Baland and Platteau (1999) — is that the effect of inequality on conservation is ambiguous. Inequality can take many forms and impact cooperation to conserve CPRs in different ways (Baland et al., 2018). With regards to endowment heterogeneity there are many promising topics for future research.

For starters, future research is required to investigate the relationship between inequality and the coordination of behavior around focal points. Starting from the premise that focal points represent plausible norms of behavior, research could measure the agreement among subjects (as a measure of salience) on the appropriateness of each plausible norm across equal and unequal groups using the coordination game created by Krupka and Weber (2013). Following the results presented in this study, the hypothesis would be that norms rated as more appropriate would enable better coordination. To alter the salience of these plausible norms, endowment heterogeneity could be generated exogenously (as in this study) or endogenously (e.g. using a real effort task), since earned wealth can shift notions about fairness.²⁵ In our current study with exogenous endowment heterogeneity, we observe coordination around the Equal Earnings norm. If endowment heterogeneity were instead generated through a real effort task, the Equal Earnings norm may fall out of favor, and we may observe coordination around the Equal Contribution norm or the Equal Proportion norm.

Beyond the underlying mechanism determining how inequality creates focal points, it is unclear whether our results hold for different levels of inequality within groups. Extreme inequality in particular may alter behavior and coordination in several ways.

For one, extreme inequality may simplify coordination. This is because endowments determine externalities and outside options. The very poor have few outside options but impose small externalities when they extract the CPR, while the very rich impose large externalities but have more outside options (Dayton-Johnson and Bardhan, 2002).²⁶ The upshot is that coordinating on the socially optimal level of extractions may be easier if the poor can simply extract at full capacity while the rich substitute away from the CPR. This in stark contrast to our design with mild inequality where Low types can still impose non-trivial external costs on High types (the symmetric Nash equilibrium in our design is 40, the Low endowment), putting pressure on High types to coordinate.

Extreme inequality may also influence peer enforcement. Baland and Platteau (1999) suggest that rich agents could use their largess to police the commons, an example of the “Olson effect” in which rich agents privately provide public goods (Olson, 1965). Results from our experiment with relatively mild inequality do not support this idea. When choosing punishment, subjects were only restricted by their initial payoffs, meaning High types typically had more power than Low types, but results shows that High were not significantly more likely to punish, nor impose significantly larger punishment. However, the picture may change if inequality is extreme. On the one hand, high-income agents may take up the role of private enforcer for the common good. On the other hand, the power asymmetry could see them crowd-out lower-income agents from the CPR.

Finally, future research can explore how inequality interacts with multiple institutions. For example, punishment in some (but not all) CPR games is more effective when combined with communication (Cason and Gangadharan, 2016; Janssen et al., 2010; Ostrom et al., 1992), while Kroll et al. (2007b) show that voting is more effective when combined with punishment in public goods games and (Bernard et al., 2013).²⁷ In a CPR with endowment heterogeneity, voting and punishment may speed up the process of coordinating around focal points and sanctioning deviations.

Online Appendix available from: http://dx.doi.org/10.1561/102.00000099_app