Incomplete punishment networks in public goods games: experimental evidence

Abundant evidence suggests that high levels of contributions to public goods can be sustained through self-governed monitoring and sanctioning. This experimental study investigates the effectiveness of decentralized sanctioning institutions in alternative punishment networks. Our results show that the structure of punishment network significantly affects allocations to the public good. In addition, we observe that network configurations are more important than punishment capacities for the levels of public good provision, imposed sanctions and economic efficiency. Lastly, we show that targeted revenge is a major driver of anti-social punishment.


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 et al. 1992;Fehr and Gächter 2000;Walker and Halloran 2004;Sefton et al. 2007, Gächter et al., 2010. These findings suggest that selfgoverned monitoring and sanctioning may play an important role in human cooperation and wellfunctioning 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. 4 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 capacities 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 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 5 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 andGächter 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), reputation networks (Milinski and Rockenbach, 2006) and leadership structures (Güth et al., 2007) all potentially serve as proximate mechanisms to enhance voluntary cooperation. 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 andCook 1993, Fatas et al. 2010) point to the fact that contribution levels may differ significantly across networks.
1 Since establishing the seminal finding that costly peer sanctioning can have a large positive impact on cooperation in social dilemmas, numerous additional studies have identified important limitations that may reduce the effectiveness of punishments and hinder the achievement of Pareto improvements through decentralized sanctioning institutions. Among the discussed limitations some particularly notable ones are the threat of counter punishments that may make people less willing to punish free-riders (Denant-Boemont et al., 2007;Nikiforakis, 2008) or lead to destructive feuds (Nikiforakis and Engelmann, 2011), and anti-socially targeted punishments (Hermann et al., 2008) that may prevent the co-existence of punishments and cooperative strategies (Rand et al., 2010). Likewise, it has been shown that the cost effectiveness of punishments plays an important role when assessing the impact of punishment strategies on cooperation and social efficiency (Egas and Riedl 2008;Nikiforakis and Normann, 2008). At the same time, however, it has been shown that various mechanisms allowing participants to effectively coordinate their punishment behavior may enhance the effectiveness of decentralized institutional arrangements (Ertan et al., 2009;Boyd et al., 2010). See Chadhauri (2010) for a recent article reviewing the experimental literature on sustaining cooperation in social dilemmas. 6 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).
More closely related to our study are experiments in which punishment opportunities in public goods settings are manipulated (Carpenter 2007a, Kosfeld et al., 2009O'Gorman et al. 2009, Reuben andNikiforakis et al., 2010;Carpenter et al. 2012;Cox et al., 2011). 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) (Carpenter 2007a, Carpenter et al. 2012. Second, a partner-matching protocol with fixed identifiers is used. 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. 2 Finally, individual punishment endowments and total punishment capacities are 7 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.

THE DECISION SETTING
This study includes data from experimental sessions conducted at Indiana University-Bloomington (U.S.) and the University of East Anglia (U.K.). In each session, 12 to 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 which of the others in the room was assigned to their group. Since no information passed across groups, each session involved 3 to 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. 3 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 individual actors, we believe that the partner-matching protocol is more suited for our purposes. Disentangling the motivation of individual actors in a public goods experiment, even if it uses stranger-matching, is very difficult. First, it is difficult to distinguish between different non-selfish motivations such as inequity-version, reciprocity, or spite. Second, other studies show that a substantial fraction of contributions are due to confusion and errors rather than non-selfish motivations (Andreoni 1995). 3 See Appendix B for the instructions. The programs were written using Z-tree (Fischbacher 2007). 8 members in their group by assigning deduction tokens to them. 4 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 3 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. 5 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. 6 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 6 tokens, which were placed in their private accounts.
Otherwise, this treatment was conducted in 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 9 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 6 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.
For control purposes, in the initial set of experiments subjects could assign a maximum of 2 deduction tokens to another group member, reducing that subjects earnings by a maximum of 6 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 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 6 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 3 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 76 four-person groups. In the experiments conducted in the U.S., 10 the conversation rate of tokens to dollars was 20 to 1. In the U.K., the conversation of tokens to pounds was 30 to 1. 7 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. 8 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.

RESULTS
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. For brevity, the analyses presented below pools the data from both experimental sites. Analyses (contained in Appendix A) indicated that our primary findings are robust to pooling/not pooling the data.

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 7 These differential exchange rates were chosen to create experimental earnings that yielded approximately the same real valued payoffs across locations. Subject's experimental earnings averaged $22 in the U.S., including a $5 show-up payment, and £15 in the U.K., including a £3 show-up payment. Sessions lasted from one to one and one half hours. 8 In the sanction treatments there are other Nash equilibria, including some that support efficient allocations. However, equilibrium strategies that support efficient allocations rely on non-credible threats to sanction free riders. sanctioning by each four-person group, 3) tokens earned by each group. Figure Table 2 presents the means and standard deviations of per-round group allocations, group earnings, and sanctions per group, pooled over decision rounds.
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.
Non-parametric statistical tests (Mann-Whitney tests) confirm the pattern of results drawn from  Relative to the no-punishment networks, group allocations are significantly higher in the complete networks (p = 0.003) and the untouchable networks (p = 0.042), but not in the pairwise networks (p = 0.371). Further, group allocations are clearly higher in the complete networks than in the pairwise networks (p = 0.010). There is no statistically significant difference between allocations in the pairwise and untouchable networks (p = 0.097).

RESULT 1:
The structure of the punishment network significantly affects public good contributions.

Incomplete 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 2 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 Figure 2b and Table 2, average group sanctions imposed in the complete and untouchable networks are similar in most rounds (Mann-Whitney p = 0.850) and remain steady at around 2.5 tokens per round. In the pairwise networks average group sanctions are lower than in the complete (p = 0.043) and the untouchable networks (p = 0.022) in all 20 rounds. Thus, network structures with greater sanctioning opportunities lead to increased levels of sanctioning.

RESULT 2:
The structure of the punishment network significantly affects sanctioning levels.

Sanctioning levels are lower in incomplete punishment networks.
While there are significant differences in group allocations and sanctioning behavior across the treatments, group earnings display a similar pattern over time. 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. Mann-Whitney tests confirm that there is no significant difference in earnings between the no-punishment network and networks with sanctions (complete, p = 0.812; pairwise, p = 0.479; untouchable, p = 0.252).
To examine whether results 1-2 are driven by the structure of the punishment networks or differences in absolute punishment capacity, we compare the pairwise networks to the pairwise-6 networks and then the untouchable networks to the untouchable-6 networks. Figures 3a-c display the trajectory of mean group allocations (3a), sanctions (3b) and earnings (3c) for the pairwise networks and the pairwise-6 networks. In summary, no statistical difference is observed in group allocations, group sanctions, and earnings; (allocations, p = 0.503), sanction, (p = 0.837), and 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 = 0.009). 13 Figures 4a-c displays the trajectory of mean group allocations (4a), sanctions (4b) and earnings (4c) for the untouchable networks and the untouchable-6 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 5 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).
RESULT 3: 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 efficiencies.

Individual Level Results
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 two following sections investigate how the network position in the pairwise and untouchable networks impacts group allocations. 10

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 14 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 either of them. Table 3 presents the results from a random effects panel 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. 11 The results indicate that both the lagged allocations of one's partner and the lagged 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 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 significantly negative in the pairwise networks (p = 0.014) and significantly positive 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).

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. 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 Figure

Patterns of Sanctioning Behavior
Pooling across treatments and observations within specified intervals, Figure 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. 13 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.
As discussed above, this study employed a partner-matching protocol with fixed identifiers. 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 networks 14 and round dummies.
Separate regressions are estimated for negative and non-negative deviations. The results in Table 6 show the usual pattern for sanctioning when deviations are below the average of the others in the group. 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. We do not find significant evidence showing that (weakly) positive deviations from the group average lead to 'anti-social' punishment. 15 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 5: Targeted revenge drives anti-social punishment in our networks.

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.     *** sig. at 1%, ** sig at 5%, * sig at 10%

Figure 1 -Punishment Networks
Notes: 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.

Appendix A1 -Testing for Location Effects
As mentioned in Section 2, we ran sessions in two locationsthe University of East Anglia, UK and Indiana University Bloomington, USAfor our initial three treatments, i.e., the complete network, pairwise network and the untouchable network. Recent work suggests that there may be systematic differences in the behavior of subjects in different countries (Hermann et. al. 2008). Before proceeding to the main analysis presented in Section 3, we first tested for potential differences in behavior of subjects in the two locations.   Figure A1. The t-tests and Wilcoxon tests suggest no significant differences between locations in allocations, sanctions and earnings. Figure A2 presents the mean allocations, sanctions and earnings of groups over time in the pairwise network treatment in both locations. In both locations, group allocations start at around 20 tokens and 35 then quickly decline. In the UK, they decline to about9 tokens by round 20 while in the US they decline to almost zero tokens, the free-riding equilibrium. Contributions in the UK are always above contributions in the US in all rounds starting very early in the game. Group sanctions begin at about 2 tokens in both locations but decline to below 1 token per round in the US, except in the last period where there is a spike. In the UK, sanctions are relatively stable between 1.5 and 2 tokens per round.
As with contributions, group sanctions are higher in the UK than in the US in almost every round.
Consistent with higher contributions and higher sanctions in the UK than in the US, there is no perceptible difference in earnings over time in the two locations.
The middle panel in Table A1 confirms the trends noted above. Mean contributions and sanctions are higher in the UK groups than in the US groups while there is almost no difference in group earnings between countries. However, the t-tests and the Wilcoxon tests indicate that none of these differences between locations is significant. The bottom panel in Table A1 confirms these trends for the untouchable treatment and the statistical tests indicate there is no significant difference in behavior of groups in the untouchable treatment in the two locations.
Our analysis thus suggests that patterns of behavior are similar across locations and that primary findings are robust to pooling data across the two locations.

B1. Instructions for the Complete Network
Thank you for coming! This is an experiment about decision-making. You will receive $5 for showing up on time. If you follow the instructions carefully, you can earn more money depending both on your own decisions and on the decisions of others.
These instructions and your decisions in this experiment are solely your private information. During the experiment you are not allowed to communicate with any of the other participants or with anyone outside the laboratory. Please switch off your mobile phone now. If you have any questions at any time during the course of this experiment, please raise your hand. An experimenter will assist you privately.

The experiment consists of twenty (20) consecutive decision rounds.
Your total earnings will be the sum of your earnings from all these rounds.
At the beginning of the experiment, participants will be randomly divided into groups of four (4) individuals. The composition of the groups will remain the same in each round. This means that you will interact with the same people in your group throughout the experiment. For record keeping purposes, the computer will randomly assign each individual in a group an ID letter, either A, B, C or D. You, and each of the other group members, will have the same ID for the rest of this experiment.
Thus, if you are assigned to be individual A in your group, your ID will be A in all 20 decision rounds.
This experiment is structured so that the other participants will never be informed about your personal decisions or earnings from the experiment. You will record your decisions privately at your computer terminal. You will be paid individually and privately in cash at the end of the experiment.
During the experiment all decisions and transfers are made in tokens (more details below). Your total earnings will also be calculated in tokens and, at the end of the experiment will be converted to Dollars at the following rate: 20 tokens = $1 45

First Stage of each round
You are a member of a group of four participants. At the beginning of each round, each member is endowed with 10 tokens. Your task is to allocate them fully or partially either into your private account or to a group account. Each token not allocated to the group account will automatically remain in your private account. Your total earnings include earnings from both your private account and the group account. All participants in your group will simultaneously face the same decision situation.

Your earnings from the private account in each round
You will earn one (1) token for each token allocated to your private account. No other member in your group will earn from your private account.

Your earnings from the group account in each round
For each token you allocate to the group account, you will earn 0.4 tokens. Each of the other three people in your group will also earn 0.4 tokens. Thus, the allocation of 1 token to the group account yields a total of 1.6 tokens for all of you together. Your earnings from the group account are based on total number of tokens invested by all members in your group. Each member will profit equally from the amount allocated to the group account. For each token allocated to the group account, each group member will earn 0.4 tokens regardless of who made the allocation. This means that you will earn from your own allocation as well as from the allocations of others.

Your total earnings in Stage 1 in each round
Your total earnings consist of earnings from your private account and the earnings from the group account.

Your earnings in Stage 1 = Earnings from your private account + Earnings from the group account
The following examples are for illustrative purposes only.
Example1. Assume that you have allocated 0 tokens to the group account. Suppose that each of the other group members has also allocated 0 tokens to the group account. Thus the total number of tokens in the group account in your group is 0. Your earnings from Stage 1 of this round will be 10 tokens (10 tokens from your private account and 0 tokens from the group account). The earnings of the other group members in Stage 1 of this round will be 10 tokens each.

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Example2. Assume that you have allocated 5 tokens to the group account. Suppose that each of the other group members has allocated 0 tokens to the group account. Thus the total number of tokens in the group account in your group is 5. Your earnings from Stage 1 of this round will be 7 tokens (= 5 tokens from your private account and 5* 0.4 = 2 tokens from the group account). The earnings of the other group members from Stage 1 of this round will be 12 tokens (= 10 tokens from the private account + 5 * 0.4 = 2 tokens from the group account) each.
Example3. Assume that you have allocated 10 tokens to the group account. Suppose that each of the other group members has also allocated 10 tokens to the group account. Thus the total number of tokens in the group account in your group is 40. Your earnings from Stage 1 of this round will be 16 tokens (= 0 tokens from your private account and 40* 0.4 = 16 tokens from the group account). The earnings of the other group members will similarly be 16 tokens each.

Second Stage of each round
After all individuals have made their decisions in the first stage, the computer will tabulate the results.
You will be informed of the total allocation to the group account and the individual allocation decisions of each group member. Group members will be identified by their IDs, which will remain the same in each round. Group members will be listed alphabetically by their IDs.
In the second stage, each person will receive an additional endowment of six tokens. You will now make a decision whether to decrease the earnings of other members in your group by assigning deduction tokens to them. Each deduction token you assign to another group member costs you 1 token and will decrease the earnings of that group member by 3 tokens. You can assign a maximum of 2 deduction tokens to any group member. If you do not want to change the earnings of a specific group member, you will assign a 0 to that group member. Any tokens not used to decrease the earnings of other group members will be kept in your private account. You will earn 1 token for each token kept in your private account.

To which group member you can assign deduction tokens depends on your ID letter as detailed below. Your ID letter also determines who can assign deduction tokens to you.
Person A can assign deduction tokens to persons B, C and D. For each of the other three group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons B, C and D is 2 each.
Person B can assign deduction tokens to persons A, C and D. For each of the other three group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons A, C and D is 2 each.

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Person C can assign deduction tokens to persons A, B and D. For each of the other three group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons A, B and D is 2 each.
Person D can assign deduction tokens to persons A, B and C. For each of the other three group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons A, B and C is 2 each.
Notice that due to the varying possibilities to assign deduction tokens to other group members, the prospect of receiving deduction tokens differs according to the ID letter. The following illustration clarifies the interaction structure at the second decisions stage. An outgoing arrowhead means that you can assign up to 2 deduction tokens to the receiving group member. An incoming arrowhead means that you can be assigned up to 2 deduction tokens by the group member from whom the arrow originates.
Figure1. Illustration of the interaction structure in the second stage For instance, consider person A in Figure 1. An outgoing arrow from A to B means that person A can assign up to 2 deduction tokens to person B. An incoming arrow from D to A means that person A can be assigned up to 2 deduction tokens by person D.

Your earnings in Stage 2 = 6 -Total number of deduction tokens used by you -3 * Total number of deductions tokens assigned to you by other group members
To summarize, your total earnings from each round will be calculated as follows: Your total earnings in each round =

Earnings from the second stage (in TOKENs)
After all participants have made their decisions in the first and second decision stage, the number of tokens you earned in the corresponding round will be displayed to you and stored in the computer.
Notice that your total calculated earnings in tokens at the end of a decision round can be negative if the costs from assigned and received deduction tokens exceed your combined earnings from the first stage and tokens kept in the individual account in the second stage.
Your earnings from earlier rounds cannot be used in the following rounds. You will receive a new endowment for the first and second decision stage in each round. The same process will be repeated for a total of 20 rounds. If your cumulative earnings from all 20 rounds at the end of the experiment are negative, the computer will automatically record zero earnings for you from the experiment. Thus, while your earnings from any particular round can be negative, your earnings from the experiment CANNOT be negative.
At any time, a history table with a summary of decisions and earnings in the previous round will be available. For each group member, the table will report the number of tokens he/she allocated to the group account in the first stage. In addition, the table will also report the number of deduction tokens assigned by a group member to every other group member. Finally, the table will also report the total number of deduction tokens received, earnings from the round and total cumulative earnings for each group member. Once again, the group members will be listed alphabetically by their ID letters. Figure   2 below presents the history table you will see.
To see the history screen, click the 'History of previous round' button at the bottom of your screen.
To continue, you must click the 'Return' button.

B2. Instructions for Paired Network Related to Stage 2 Second Stage of each round
After all individuals have made their decisions in the first stage, the computer will tabulate the results.
You will be informed of the total allocation to the group account and the individual allocation decisions of each group member. Group members will be identified by their IDs, which will remain the same in each round. Group members will be listed alphabetically by their IDs.
In the second stage, each person will receive an additional endowment of six tokens. You will now make a decision whether to decrease the earnings of other members in your group by assigning deduction tokens to them. Each deduction token you assign to another group member costs you 1 token and will decrease the earnings of that group member by 3 tokens. You can assign a maximum of 2 deduction tokens to any group member. If you do not want to change the earnings of a specific group member, you will assign a 0 to that group member. Any tokens not used to decrease the earnings of other group members will be kept in your private account. You will earn 1 token for each token kept in your private account.

To which group member you can assign deduction tokens depends on your ID letter as detailed below. Your ID letter also determines who can assign deduction tokens to you.
Person A can assign deduction tokens to person B alone. You will decide how many deduction tokens to assign person B. The maximum number of deduction tokens you can assign to persons B is 2. Four tokens out of your endowment of 6 tokens will automatically be transferred to your private account.
Person B can assign deduction tokens to person A alone. You will decide how many deduction tokens to assign person A. The maximum number of deduction tokens you can assign to persons A is 2. Four tokens out of your endowment of 6 tokens will automatically be transferred to your private account.
Person C can assign deduction tokens to person D alone. You will decide how many deduction tokens to assign person D. The maximum number of deduction tokens you can assign to persons D is 2. Four tokens out of your endowment of 6 tokens will automatically be transferred to your private account.

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Person D can assign deduction tokens to person C alone. You will decide how many deduction tokens to assign person C. The maximum number of deduction tokens you can assign to persons C is 2. Four tokens out of your endowment of 6 tokens will automatically be transferred to your private account.
Notice that due to the varying possibilities to assign deduction tokens to other group members, the prospect of receiving deduction tokens differs according to the ID letter. The following illustration clarifies the interaction structure at the second decisions stage. An outgoing arrowhead means that you can assign up to 2 deduction tokens to the receiving group member. An incoming arrowhead means that you can be assigned up to 2 deduction tokens by the group member from whom the arrow originates.

Figure1. Illustration of the interaction structure in the second stage
For instance, consider person A in Figure 1. An outgoing arrow from A to B means that person A can assign up to 2 deduction tokens to person B. An incoming arrow from C to A means that person A can be assigned up to 2 deduction tokens by person C.

B3. Instructions for Untouchable Network related to Stage 2 Second Stage of each round
After all individuals have made their decisions in the first stage, the computer will tabulate the results.
You will be informed of the total allocation to the group account and the individual allocation decisions of each group member. Group members will be identified by their IDs, which will remain the same in each round. Group members will be listed alphabetically by their IDs.
In the second stage, each person will receive an additional endowment of six tokens. You will now make a decision whether to decrease the earnings of other members in your group by assigning deduction tokens to them. Each deduction token you assign to another group member costs you 1 token and will decrease the earnings of that group member by 3 tokens. You can assign a maximum of 2 deduction tokens to any group member. If you do not want to change the A B C D 51 earnings of a specific group member, you will assign a 0 to that group member. Any tokens not used to decrease the earnings of other group members will be kept in your private account. You will earn 1 token for each token kept in your private account.
To which group member you can assign deduction tokens depends on your ID letter as detailed below. Your ID letter also determines who can assign deduction tokens to you.
Person A can assign deduction tokens to persons B and C. For each of these two group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons B and C is 2 each. Two tokens out of your endowment of 6 tokens will automatically be transferred to your private account.
Person B can assign deduction tokens to persons C and A. For each of these two group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons C and A is 2 each. Two tokens out of your endowment of 6 tokens will automatically be transferred to your private account.
Person C can assign deduction tokens to persons A and B. For each of these two group members, you will decide how many deduction tokens to assign him/her. The maximum number of deduction tokens you can assign to persons A and B is 2 each. Two tokens out of your endowment of 6 tokens will automatically be transferred to your private account.
Person D can NOT assign deduction tokens to anyone. You entire endowment of 6 tokens will be transferred to your private account.
Notice that due to the varying possibilities to assign deduction tokens to other group members, the prospect of receiving deduction tokens differs according to the ID letter. The following illustration clarifies the interaction structure at the second decisions stage. An outgoing arrowhead means that you can assign up to 2 deduction tokens to the receiving group member. An incoming arrowhead means that you can be assigned up to 2 deduction tokens by the group member from whom the arrow originates. For instance, consider person A in Figure 1. An outgoing arrow from A to B means that person A can assign up to 2 deduction tokens to person B. An incoming arrow from C to A means that person A can be assigned up to 2 deduction tokens by person C.