1 Introduction

There is widespread evidence that the availability of costly peer sanctioning can have a large positive impact on cooperation in social dilemma settings (e.g., Ostrom 1990; Ostrom et al. 1992; Fehr and Gächter 2000; Walker and Halloran 2004; Sefton et al. 2007). These findings suggest that self-governed monitoring and sanctioning may play an important role in human cooperation and well-functioning of modern societies. However, the prevailing evidence is mainly based on the comparison of two extreme cases; all individuals can punish and be punished by other individuals in a group versus a situation where no one can punish. These criteria are typically not met in the field where various factors such as physical distance, endowments and status, and the social network of actors regularly limit punishment opportunities.

Punishment networks, which define who can punish whom, may play a nontrivial role for inducing more efficient provision of public goods or appropriation from common-pool resources. In particular, it seems plausible that denser punishment networks, where a larger fraction of actors can punish each other, deter actors more effectively from non-cooperative behaviors. This increased deterrence in denser networks may be associated with the threat of being punished by more agents and/or the possibility of larger combined punishment capacity. However, it seems equally plausible that denser punishment networks may deter actors less effectively from non-cooperative behaviors if actors believe that the threat of being punished diminishes as the number of potential targets increases and effective coordination of punishment becomes more difficult. In addition, the increasing number of potential targets and limited individual capacities to sanction may reduce the severity of assigned sanctions. Taken together, there is very little direct evidence on how the network structure and punishment capacity impact public good provision, imposed sanctions and economic efficiency.

In this study, we provide new empirical evidence on the role of punishment networks for facilitating cooperation. We employ a public goods experiment in which we manipulate the structure of punishment networks and punishment capacities. Contribution and punishment decisions are examined across twenty rounds of repeated play in groups of four players who have fixed identifiers. Four networks are examined: a complete punishment network, a ‘pairwise’ punishment network, an ‘untouchable’ punishment network and a no-punishment network. In the pairwise network, the group of four is divided into two pairs and punishment can only take place within pairs, although contributions affect the entire group. In the untouchable network, there are three agents that can punish and be punished by each other and one agent who cannot punish or be punished.

By reducing the number of players who can punish a player, the two incomplete networks (pairwise and untouchable) reduce the total capacity of players to impose and receive punishment. For this reason, an additional treatment is conducted in each of the incomplete networks such that punishment capacities were as high as in the complete network. Individual punishment capacities are manipulated in these two networks in order to investigate if observed behavior is driven by the structure of the punishment network or punishment capacity.

These punishment networks were selected for the following reasons. First, arguably, the pairwise networks constitute the most transparent cases to examine issues of targeting sanctions, reputation formation, and limited scope of sanctions. The untouchable networks were selected based on observations from the field where it is common that some agents are temporarily or permanently isolated from others, but cannot be excluded from the benefits of public goods or common-pool resources. Complete and no punishment network conditions are created as benchmarks and to better link our findings to the existing experimental literature. The investigation of punishment behavior in incomplete networks connects our study to numerous examples of common-pool resource management and public good provision settings where the geographical structure and state borders may limit stakeholders’ opportunities to sanction each other. At the same time, many of the international agreements designed to protect natural resources and curb environmental deterioration implement governance structures that often allow for accurate monitoring of contributions but limited opportunities to punish detached actors.

A primary finding of this study is that the greater the number of people who can punish and be punished, the greater the contributions to the public good and the greater the amount of punishment used in the group. Further, high contributions are sustained only in the complete and untouchable networks. In addition, the capacity for one individual to punish another plays a less important role on aggregate contribution levels than the network configuration. In particular, higher punishment capacities are unable to stem the observed decline in contributions in the pairwise network, and also play an insignificant role in the untouchable network. Finally, consistent with previous findings, low and high contributors are punished (Hermann et al. 2008), a finding that is consistent with targeted revenge.

This study contributes to the literature testing the effectiveness of various institutional arrangements to overcome the regularly observed sub optimality of voluntary contributions. Among the large body of proposed institutional solutions to the problem of free-riding, opportunities to communicate (Isaac and Walker 1988; Ostrom et al. 1992; Bochet et al. 2006), costly peer punishments (Ostrom et al. 1992, Fehr and Gächter 2000), verbal sanctioning (Masclet et al. 2003), ostracism (Cinyabuguma et al. 2005), combined punishment and reward schemes (Andreoni et al. 2003; Gürerk et al. 2006; Sefton et al. 2007; Leibbrandt and López-Pérez 2014), reputation networks (Milinski and Rockenbach 2006) and leadership structures (Güth et al. 2007) all potentially serve as proximate mechanisms to enhance voluntary cooperation.Footnote 1

In addition, this study connects to an emerging literature examining the role of social and geographic network structures on public good provision when punishment opportunities are absent. Theoretical investigations (Bramoullé and Kranton 2007) and experimental evidence (Yamagishi and Cook 1993; Fatas et al. 2010) point to the fact that contribution levels may differ significantly across networks. Differences in contributions across such networks are explained by conditionally cooperative responses to the restricted spread of information about individual contributions (Fatas et al. 2010).Footnote 2

More closely related to our study are experiments in which punishment opportunities in public goods settings are manipulated (Carpenter 2007a; Kosfeld et al. 2009; O’Gorman et al. 2009; Reuben and Riedl 2009; Nikiforakis et al. 2010; Carpenter et al. 2012; Cox et al. 2013). Reuben and Riedl (2009) study the effectiveness of punishment in privileged groups where some group members generate positive returns from public good contributions. Their findings indicate that punishment is less effective in privileged groups as compared to normal groups. Kosfeld et al. (2009) investigate institution formation in social dilemmas where a subset of players can form a sanctioning institution, while their contributions benefit the outsiders who do not enter the institution. Nikiforakis et al. (2010) vary the effectiveness of punishments across individuals. Their results suggest that institutions with asymmetric sanctioning power can be equally successful in fostering cooperation and efficiency than their symmetric counterparts. Carpenter et al. (2012) manipulate monitoring opportunities and show how properties from graph theory can organize the data patterns that arise in their public goods experiments.

This study differs in several aspects from the previous literature. First, previously unexplored network structures are examined in settings where decision makers receive complete information about individual contributions, sanctions imposed, and sanctions received for all group members. This contrasts with other studies that investigate the joint effect of information dissemination and punishment opportunities in networks where group members do not receive information on individual behavior outside their network (Carpenter 2007a; Carpenter et al. 2012). Second, we use a partner-matching protocol with fixed identifiers. The advantage of fixed identifiers is that this information condition captures the essence of many real networks where individuals have stable positions within a fixed group, not simply a network architecture describing how a random group of individuals occasionally link.Footnote 3 Finally, individual punishment endowments and total punishment capacities are controlled for across groups. Thus, in contrast to many studies, we are able to identify the role of the punishment network and can rule out potential endowment effects.

2 The decision setting

This study includes data from experimental sessions conducted at Indiana University-Bloomington (US) and the University of East Anglia (UK). In each session, 12–20 subjects were recruited from subject databases that included undergraduates from a wide range of disciplines. Via the computer, subjects were privately and anonymously assigned to four-person groups and remained in these groups throughout the 20 rounds in a session. No subject could identify the others in the room that were assigned to their group. Since no information passed across groups, each session involved 3–5 independent groups. At the beginning of each session, subjects privately read a set of instructions, which were then summarized publicly by a member of the research team.Footnote 4 Subjects then took a post instruction quiz and were not allowed to continue until all answers were correct. Subjects made all decisions privately.

Stage 1 of each decision round was a linear VCM game. At the beginning of stage 1, each subject was endowed with ten tokens to be allocated between a private account and a group account. For each token placed in his or her private account a subject received 1 token in payment. For each token placed in the group account, each group member received 0.4 tokens in payment. After all subjects had made their decisions in stage 1, they were informed of the aggregate allocations to the group account, and the allocation of each member of their group identified by an anonymous ID letter (A, B, C, or D), which remained the same during all decision rounds.

In stage 2 of each decision round each subject received an additional endowment of six tokens. Subjects were informed that they would make a decision of whether to decrease the earnings of other members in their group by assigning deduction tokens to them.Footnote 5 The instructions used neutral language. Each deduction token assigned by a group member to another group member cost the initiator 1 token and decreased the earnings of the recipient by three tokens. Any tokens not used to decrease the earnings of other group members were kept in the subject’s private account.

Following stage 2 decisions, each subject received information about the contribution and sanction decisions of every other subject in his/her group.Footnote 6 More specifically, each subject reviewed a table which displayed the group account allocation of each subject in their group and the number of deduction tokens each subject assigned to each other subject in the group identified by ID letters. This table also displayed current round and cumulative earnings for each subject. At any point in the experiment subjects could review this same information from the prior round, giving them a complete history of individual decisions from the prior round before making their current round decisions. Thus, unlike in many earlier decision settings that have investigated the use of sanctioning mechanisms, it was feasible for subject-specific reputations to develop across rounds.Footnote 7 The network treatment conditions are the primary rationale for this particular parameterization.

No sanctions were allowed in the benchmark treatment, the no-punishment network. In stage 2, subjects were simply given an additional six tokens, which were placed in their private accounts. Otherwise, this treatment was conducted in the same manner as the treatments that allowed for sanctioning opportunities. As noted in the introduction, there were three treatment conditions that allowed for sanctions: a complete network, a pairwise network, and an untouchable network. Experimental conditions varied only in terms of opportunities for sanctioning defined by the network linkages. In the complete network condition, subjects had the opportunity to reduce the earnings of all other group members. In the pairwise network condition, subjects A and B had the opportunity to reduce the earnings of each other, but not C and D. Likewise, subjects C and D had the opportunity to reduce the earnings of each other, but not A and B. In the untouchable network condition, subjects A, B, and C had the opportunity to reduce the earnings of each other, but not subject D. Further, subject D did not have the opportunity to reduce the earnings of any group member. For control purposes, subject D automatically had six tokens allocated to their private account.

Figure 1 illustrates our network treatments. In all network treatments information flow was held the same. Only the punishment opportunities depended on the network. In the figures, an incoming arrow denotes that a player can be punished by the player from whom the arrow originates. An outgoing arrow denotes that a player can punish the receiving group member.

Fig. 1
figure 1

Punishment networks. In all treatments information flow was held the same, indicated by the lines between players. Every player received information about the contribution and punishment decisions of every other player in her group. Only the punishment opportunities depended on the network. An incoming arrow denotes that a player can be punished by the player from whom the arrow originates. An outgoing arrow denotes that a player can punish the receiving group member

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For control purposes, in the initial set of experiments subjects could assign a maximum of two deduction tokens to another group member, reducing that subjects earnings by a maximum of six tokens, regardless of the network structure. Subjects in the pairwise network automatically had 4 tokens allocated to their private accounts in stage 2 while subjects A, B and C in the untouchable network automatically had 2 tokens allocated to their private accounts in stage 2. Players could use the remaining tokens to sanction players in their network. Thus, in the initial set of experiments, the maximum sanction that a subject could impose on another subject was held constant across decision rounds, while the maximum number of punishment tokens a subject could receive varied across networks.

An additional set of experiments was conducted in the pairwise and untouchable networks, where the maximum number of deductions tokens that a subject could receive was equal to that of the complete network. In the pairwise-6 treatment each subject could impose up to six punishment tokens on the subject with whom they were paired. In the untouchable-6 treatment, the three subjects in the punishment network could impose up to three punishment tokens on the other two subjects in their network. Thus, in these treatment conditions, subjects in the networks could have their earnings reduced from punishments by a maximum of 18 tokens, the same as in the complete network condition.

Table 1 presents summary information related to subject groups in each of the conditions. In aggregate, data were collected from 84 four-person groups. In the experiments conducted in the US, the conversion rate of tokens to dollars was 20 to 1. In the U.K., the conversion of tokens to pounds was 30 to 1.Footnote 8

Table 1 Design information for network conditions
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In all treatment conditions, subjects played a finitely repeated game with a known final round. Under the assumption that it is common knowledge that subjects maximize own-earnings, the theoretical prediction is straightforward. The subgame perfect Nash equilibrium for each treatment condition calls for zero allocations to the group account and no-sanctions.Footnote 9 As noted earlier, however, experimental studies of the linear VCM game typically find that the level of cooperation observed is not consistent with equilibrium predictions of zero provision of the group good. Moreover, other studies have shown that subjects often pay to sanction other participants when the opportunity is available. However, at the same time subjects react to changes in the price and effectiveness of punishment (Carpenter 2007b), suggesting that players strategically assess the cost and benefits of various sanctioning strategies. At the core of our investigation is the question how the network structure and disposable punishment capacities affect these considerations.

3 Results

As noted in Sect. 2, experimental sessions for the no-punishment, complete, pairwise, and untouchable network conditions were conducted in two locations, the University of East Anglia, UK and Indiana University Bloomington, USA. Recent work suggests that there may be systematic differences in the behavior of subjects in different countries (Hermann et. al. 2008). Controlling for treatment condition, we tested for differences in behavior in the two locations. A detailed analysis is available in Sect. A of the Supplementary Material. In summary, the various tests confirm that there are no statistically significant differences in group allocations and earnings between the two locations. In addition, within each of the three treatments with sanctioning opportunities, the average level of sanctions used by groups is not different between locations. The analysis presented below therefore pools the data from both experimental sites. Results are first presented at the group level, followed by analyses at the individual level. We begin with a graphical presentation and summary statistics which focus on pooled data from the initial set of network conditions and the pairwise-6 and untouchable-6 networks.

3.1 Group level results

The discussion of results from the initial treatment conditions focuses on three key outcome variables: (1) tokens allocated to the group account by each four-person group, (2) total tokens used for sanctioning by each four-person group, (3) tokens earned by each group. Figure 2a displays the trajectory, across decision rounds, of mean group allocations, Fig. 2b of sanctions, and Fig. 2c of earnings for the complete networks (mean across 17 groups), the pairwise networks (14 groups) and the untouchable networks (15 groups). Mean group allocations and earnings for the no-punishment networks (15 groups) are also presented. To complement the results displayed in Fig. 2a–c, Table 2 presents the means and standard deviations of per-round group allocations, group earnings, and sanctions per group, pooled over decision rounds.

Fig. 2
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a–c Allocations, sanctions and earnings: initial punishment networks

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Table 2 Summary statistics: group level data
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In all treatments, average group account allocations start at around 50 % of the group endowment of 40 tokens. In the no-punishment networks, allocations decline over time to levels close to the Nash equilibrium allocation of zero. In the complete networks, allocation levels increase slightly and are maintained at around 25 tokens throughout. In the untouchable networks group allocations remain steady at around 20 tokens across rounds 1–18. However, allocations are always lower than those in the complete networks. Allocation levels in the pairwise networks are very similar to those in the no-punishment networks, though they are slightly higher after round 5.

To complement the graphical presentations, we present evidence below from non-parametric Mann–Whitney tests of differences in behavior across treatments.Footnote 10 In our experiment, groups make decisions independently of other groups as they only receive information about themselves. However, a group’s decisions are not independent over the 20 rounds in the experiment. Thus the average (allocations, sanctions or earnings) of a group over all 20 rounds serves as an independent observation for these tests. The tests confirm the pattern of results drawn from Fig. 2a–c. Relative to the no-punishment networks, group allocations are significantly higher in the complete networks (p = 0.0006) and the untouchable networks (p = 0.019), but not in the pairwise networks (p = 0.827). Further, group allocations in the complete networks are significantly higher than in the pairwise networks (p = 0.009) but not in the untouchable networks (p = 0.117). The difference between allocations in the pairwise and untouchable networks is also not statistically significant (p = 0.097).

Result 1: The structure of the punishment network significantly affects public good contributions. Incomplete pairwise punishment networks are less effective in increasing public goods contributions.

We next turn to punishment behavior. Recall, in the initial punishment network conditions, subjects were constrained to use no more than two tokens in sanctioning another individual, implying that the number of sanctions that could be imposed varied across network conditions. Yet, as can be seen from Fig. 2b and Table 2, average group sanctions imposed in the complete and untouchable networks are similar in most rounds (p = 0.850) and remain steady at around 2.5 tokens per round. In the pairwise networks average group sanctions are significantly lower than in the complete network (p = 0.043) and the untouchable network (p = 0.022). Thus, the two network structures with greater sanctioning opportunities lead to increased levels of sanctioning in relation to the pairwise networks.

Result 2: The structure of the punishment network significantly affects sanctioning levels. Sanctioning levels are lower in incomplete pairwise punishment networks.

While there are significant differences in group allocations across the treatments, after accounting for the costs of sanctioning, there is some evidence that group earnings in the sanctioning networks are marginally lower (or no higher) than in the no-punishment networks. More specifically, earnings in the no-punishment networks are higher than those in the other three networks in the first few rounds and in the last round. However, between rounds 5 and 19, there is no systematic difference in earnings across network conditions. The statistical tests confirm that there is no significant difference in earnings between the no-punishment networks and the complete and untouchable networks (p = 0.533 and p = 0.290 respectively). The non-parametric test suggests a significant difference between the no-punishment networks and the pairwise networks (p = 0.049). This difference, however, is not robust to a standard t test (p = 0.243) or to a group-level panel regression where the baseline is the no-punishment treatment (p = 0.219 for the pairwise treatment dummy).

Result 3: After accounting for the costs of sanctioning, overall earnings across punishment networks and the no-punishment network are similar.

To examine whether results 1–3 are driven by the structure of the punishment networks or differences in absolute punishment capacity, we compare behavior from the pairwise networks to the pairwise-6 networks and the untouchable networks to the untouchable-6 networks. Figure 3a–c display the trajectory of mean group allocations (3a), sanctions (3b) and earnings (3c) for the pairwise networks and the pairwise-6 networks. Table 2 presents mean and standard deviations for both networks. In summary, no statistically significant difference is observed in group allocations, group sanctions, and earnings (allocations, p = 0.503; sanction, p = 0.837; earnings, p = 0.471). In addition, despite the identical group punishment capacity between the pairwise-6 and complete networks, contributions in the pairwise-6 networks are significantly lower than in the complete networks (p = 0.069).

Fig. 3
figure 3

a–c Allocations, sanctions and earnings: pairwise and pairwise-6 networks

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Figure 4a–c displays the trajectory of mean group allocations (4a), sanctions (4b) and earnings (4c) for the untouchable networks and the untouchable-6 networks. Table 2 presents mean and standard deviations for both networks. Group allocations start out higher in the untouchable-6 networks but by round 15, there is no discernible difference in allocations. Interestingly, sanctioning is not higher but slightly lower in the untouchable-6 networks in all but five rounds. The combination of higher group allocations and lower sanctions across most decision rounds implies that earnings are somewhat higher in the untouchable-6 networks. However, there are no statistically significant differences between the two untouchable conditions (allocations, p = 0.452; sanctions, p = 0.253; earnings, p = 0.312).

Fig. 4
figure 4

a–c Allocations, sanctions and earnings: untouchable and untouchable-6 networks

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Result 4: At the group level, the structure of the punishment network is more important than the absolute punishment capacity in determining group account allocations, sanctions, and earnings.

3.2 Individual level results in incomplete networks

To complement the group level analysis, we turn to an analysis of decisions of individual group members in the incomplete networks. The nature of individual behavior in repeated public goods settings is often characterized as conditional cooperation. In incomplete networks, the network structure and players’ positions in the network are likely to influence how they adjust their behavior to that of the other group members. To better understand the effect of changing network structures on the nature of conditional cooperation, the analyses in the following two sections investigate how the network position in the pairwise and untouchable networks impacts group allocations.Footnote 11

3.2.1 Individual decisions in the pairwise networks

It is an open question whether and to what extent individuals’ allocations are influenced by the decisions of subjects that are linked to the punishment network and by the decisions of the other subjects outside the punishment network. More precisely, in the pairwise networks, subject A might be influenced by the allocation of subject B and vice versa (similarly for subjects C and D). However, in our experiment, each individual has information on the decisions of all others in his/her group. Thus, it is also possible that, within a group, subject A might be influenced by the decisions of subjects C and D even though he/she cannot be sanctioned by them.

Table 3 presents the results from a regression of individual allocations in a model incorporating the following explanatory variables: lagged allocation of subject i, lagged deviation from the subject with whom subject i is paired in the network, lagged deviation from the mean group allocation of the other pair in the group, lagged sanctions received by i, and round dummy variables. The table reports robust standard errors clustered on independent groups. We estimated an OLS regression, a random effects panel regression and a Tobit regression to account for censoring of the observations. The results are qualitatively the same in all three models. For the sake of brevity, we only report the results from the panel regression. The results indicate that both the lagged deviation in allocation from that of one’s partner and the lagged deviation from the average allocation of the other pair significantly influence one’s allocation decisions (p < 0.001 for both coefficients) and that the magnitudes are similar (coefficients for pairwise network are −0.273 and −0.256, respectively, and coefficients for the pairwise-6 network are −0.138 and −0.178, respectively).

Table 3 Individual allocations in the pairwise and the pairwise-6 networks
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Table 3 highlights an additional insight in regard to the effect of received sanctions on allocations to the group account. While the variable lagged sanction received is positive, but insignificant, when pooling both pairwise networks, this variable is negative and significant in the pairwise networks (p = 0.014) and positive and significant in the pairwise-6 networks (p = 0.002). This suggests that in the pairwise network, sanctions have a negative impact on contributions when the punishment capacity is small (for every unit of sanctioning received contributions are decreased by 0.418 token); but a positive impact on contributions when the punishment capacity is large (for every unit of sanctioning received contributions are increased by 0.295 tokens).

3.2.2 Individual decisions in the untouchable networks

In the untouchable and the untouchable-6 networks, subjects assigned the positions of A, B or C are allowed to sanction each other. Subjects assigned the position D (the untouchable) face no threat of receiving sanctions. In the analysis below, we investigate the determinants of the allocation decisions of subjects in the A, B, and C positions separately from those in the D position.

Figure 5a and b present the trajectory of mean allocations and earnings by subjects assigned to the A, B, C and D positions across decision rounds. As shown, there is a pronounced decrease in the group account allocations for the subjects in the D position, relative to those in the A, B, and C positions. The mean allocation per round by subjects in the A, B and C positions is 5.89 tokens while the mean per round allocation of subjects in the D position is 3.85 tokens (n = 26 groups, p = 0.017). Since subjects in the untouchable position also do not spend resources on sanctioning, they earn significantly more than the other group members as seen from the second panel of Fig. 5. The mean per round earnings of subjects in the A, B and C positions is 15.98 tokens while the mean per round earnings of subjects in the D position is 20.75 tokens (n = 26 groups, p < 0.000). Interestingly, the presence of an untouchable does not appear to have a significant detrimental effect on the willingness to contribute by the other subjects in the same group. There is no significant difference between the mean group account allocation by subjects in the A, B and C positions (5.89 tokens) in comparison to the mean allocation of subjects in the complete networks of 6.50 tokens (ncomplete = 17, nuntouchables = 26, p = 0.358).

Fig. 5
figure 5

a, b Allocations and earnings by network position: combined untouchable networks

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To examine more closely the factors that influence individual allocations of subjects in the A, B and C positions, Table 4 reports the results from a random effects panel data regression of individual allocations on: the one-period lagged allocation of individual i, the one-period lagged deviation of i’s allocation from the allocation of D, the one-period lagged deviation of i’s allocation from the average allocation of the other members of his punishment network, a one-period lagged variable of sanctions received, and round dummies. The table reports robust standard errors clustered on independent groups.

Table 4 Individual allocations (A, B, C): untouchable and untouchable-6 networks
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In summary, allocations of subjects attached to the punishment networks are significantly influenced by their lagged allocations (p < 0.001) and the deviation of their lagged allocations from the average allocations of others in the punishment network (p < 0.001). In addition, their allocations are also negatively influenced by the deviation of their lagged allocations from the allocation of the untouchable (p < 0.001) suggesting that the untouchable can trigger higher contributions of the subjects in the punishment network.Footnote 12 Similar to the pairwise networks, punishment capacity appears to determine whether receiving sanctions has a negative (if capacity is small) or positive (if capacity is large) impact on contributions.Footnote 13

Finally, Table 5 presents random effects estimates for the determinants of the allocations of subjects assigned to the untouchable position, D, on the one-period lagged allocation of individual i, the one-period lagged deviation of i’s allocation from the average allocation of others in the same group, and round dummies. As shown, the allocations of the subjects in the untouchable position are mostly influenced by lagged allocations. The variable, lagged deviation from mean allocations of other subjects in the group, is negative for both untouchable networks and highly significant when pooling data from the untouchable and untouchable-6 networks (p = 0.009).

Table 5 Individual allocations (D): Untouchable and Untouchable-6 networks
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Result 5: Subjects condition their contribution on the behavior of subjects in and outside their punishment network.

3.2.3 Patterns of sanctioning behavior

Pooling across treatments and observations within specified intervals, Fig. 6 shows the relationship between average sanctions received by individuals and the deviation of their group allocation from the average allocations of others in the group.Footnote 14 Also reported are the number of instances in which sanctions were imposed within each interval. Mean sanctions received are larger when a subject’s allocation is below the average allocation of others. Importantly however, there is evidence of ‘anti-social’ punishment: some subjects are sanctioned even when their allocations are above the mean of others.

Fig. 6
figure 6

Mean sanctions received by individuals

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As discussed above, this study employed a matching protocol with fixed identifiers for each decision maker in a group. An advantage of this protocol is that it captures a critical informational component of some networks. More precisely, unlike previous studies examining sanctioning, this protocol allows for sanctioning imposed on subject i by subject j to be based directly on lagged sanctions imposed by i on j. Thus, linkages between sanctions imposed and lagged sanctions received between pairs of subjects within networks (referred to as ‘sanctioning pairs’) can be examined.

Table 6 presents regressions of individual sanctions imposed on subject i by subject j as a function of deviations in contributions by i from others in the group, one period lagged sanctions imposed by i on subject j, treatment dummies for the pairwise and untouchable networksFootnote 15 and round dummies. Separate regressions are estimated for negative and non-negative deviations. The table reports robust standard errors clustered on independent groups. The results in Table 6 show the usual pattern for sanctioning when deviations are below the average of the others in the group.Footnote 16 Players are punished for low contributions and they receive higher sanctions the lower their contributions are below the average; players receive an additional 0.9 tokens in sanctions for every token they are below the average.

Table 6 Evidence on targeted revenge in sanctioning pairs
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We do not find significant evidence showing that (weakly) positive deviations from the group average lead to ‘anti-social’ punishment.Footnote 17 However, there is strong evidence of targeted revenge. Players receive sanctions from those they sanctioned in the previous round. Such targeted revenge occurs independently of whether a subject’s contribution is greater (positive deviation) or smaller (negative deviation) than the average of other group members.

Result 6: Targeted revenge drives anti-social punishment in our networks.

4 Conclusions

This study contributes to the literature on sanctioning behavior in social dilemma settings by examining the influence of alternative linkages between subjects that restrict the directional flow of endogenously imposed sanctions, as well as the capacity to sanction at the individual and group level. We find clear evidence that the structure of punishment network affects public good contributions and that the network configuration is more important than the absolute punishment capacity for public good provision, imposed sanctions and economic efficiency. In addition, our experimental design renders it possible to identify targeted revenge as a main driver of anti-social punishment.

The results of this study may have implications for public policy and organizational thinking related to the pervasive conflict of individual interest and collective efficiency. In a world where natural obstacles and manmade institutions limit stakeholder’s opportunities to sanction other actors, a proper understanding of underlying group structures and how individual actors connect to each other is crucially important when trying to understand the nature of voluntary cooperation. This study suggests that the nature of incomplete sanction networks may be more important than the group’s overall capacity to sanction. This result raises the question of whether and how collective action groups in the field can develop institutions or social norms to overcome such incompleteness.