Research across disciplines has long endeavored to understand the mechanisms through which cooperation emerges and is sustained. Much of this research analyzes the behavior of the individual, and attempts to understand why an individual would bear a cost for the benefit of others in the absence of a direct benefit to the individual. Institutional arrangements, often manifested through the opportunity to punish free riders, have been proposed as mechanisms to encourage and maintain cooperation1,2,3. More recently, an area of focus has been explaining cooperative behavior through the relationships between people, including those not directly involved in the exchange. For example, those who are genetically related to one another are more likely to cooperate with one another4,5. This work has investigated how social networks may promote or depress levels of cooperation, depending on the dynamics within them. Indeed, theoretical models of cooperation suggest that social networks may enable cooperation to evolve and endure6,7,8. However, research has thus far not investigated how institutional arrangements interact with networks to affect cooperation.

The opportunity to punish is frequently theorized to represent an institutional choice that enables the sanctioning of free-riders1. Theoretical models suggest that altruistic punishment is evolutionarily stable9 and effective at promoting cooperation2,3. In one-shot experiments, altruistic punishment has been shown to significantly increase cooperative behavior10,11,12,13,14. People often pay a personal cost to punish the uncooperative behavior of others, inducing future cooperation. In one-shot interactions punishment is thought to be altruistic, as it is not possible for the future cooperation of the punished individual to directly benefit the punisher. Importantly, the effect of punishment on uncooperative behavior varies depending on the cost and impact of punishment12. In particular, cooperation is best maintained when punishment is low-cost enough to be used with frequency and the impact of punishment is sufficient to dissuade free-riding, but when the impact of punishment is limited it is no longer effective at dissuading uncooperative behavior. Whether the relationship between the impact of punishment on individual behavior in turn affects social network dynamics surrounding cooperation is thus far unknown.

There are various explanations for why cooperative behavior may spread in networks. For example, research has shown that when one individual acts in an altruistic way, others who view that altruism may be more likely to also behave altruistically in the future15,16,17. Similarly, research has often shown that people’s cooperative behavior is conditional on the behavior of others, in which people give more when others have done so18,19. Participants give more when others do so, perhaps because the social norm around giving is stronger. Theoretical models suggest that norms surrounding cooperation may emerge in small-scale groups and such norms are effective at promoting cooperation between group members20. These mechanisms suggest that social learning about cooperative behavior may vary depending on how behavior is impacted by the institutional arrangements that govern game play. Because the effectiveness of punishment impacts cooperation overall it may similarly impact the extent to which social norms are established and therefore the extent to which cooperative behavior spreads through the network.

One mechanism through which cooperative behavior may spread through social networks is through imitation. According to social learning theory21 people learn about the behavior of others through direct experience. The theory posits that when we observe the behavior of others and view it in a positive light, we may be more likely to imitate that behavior. Observation of others may affect expectations of what is an acceptable way to behave through a change in our beliefs about social norms about cooperation19,22,23,24. Importantly, a review of studies of cooperation showed that social sanctions (in behavioral economic games these are manifested through punishments from one individual to another) are crucial for norm enforcement19. Similarly, survey work25 shows that although people have varying normative views of cooperation, that in games with punishment stable contribution patterns emerge. If cooperative behavior spreads through networks in part because of the development or updating of social norms, then the institutions that govern game play, particularly concerning the costs and impacts of social sanctioning, may substantially impact the degree to which cooperation spreads from person-to-person.

In a typical behavioral public goods experiment it is clear to see how this may take place. The public goods game environment is new to most players, so although norms about cooperation in general may be familiar to a participant, how those norms may apply to the behavioral game may be uncertain. If so, observation of the game play of those a player interacts with may be influential for the development of a norm about what levels of contribution are normative in the context of the game. Specifically, in a given round of the experiment, a player may observe that one of the other participants in her group has contributed to the public good at a high level. In this scenario, she may be more likely to give at a high level in subsequent rounds of the game because she has updated her beliefs about what levels of contribution are normative. In versions of the experiment in which punishment is possible the development of norms is likely to happen more quickly. This is because social sanctioning may reinforce normative behavior – high contributors are typically not punished, but low contributors are more frequently, which reinforces a norm of acceptable levels of cooperation. In this way, institutional arrangements may impact how quickly norms are developed, which may in turn affect the degree to which the behavior of others is impactful.

Recent work has extended individual-level experiments on cooperation in the lab by investigating cooperation in social networks26,27,28,29,30,31,32,33,34,35,36,37. Much of this work investigates how the behavior of others in the game governs tie choice29,30,31,32,33,34 or is affected by existing ties4,5,26, and the subsequent levels of cooperation in future rounds of the game. However, this work does not investigate how the parameters of game play, such as the cost and impact of punishment, affect network dynamics related to cooperation. Because institutional arrangements are known to affect norms about cooperation, and norms are known to be one mechanism through which behaviors spread from person to person38, a question emerges about the extent to which institutional arrangements affect the spread of cooperation in social networks.

This study extends our understanding of cooperation in social networks in two important ways. First, the impact of punishment varies across versions of the experiments analyzed here. Although previous work has established that the impact of punishment has important consequences for the level of cooperation at the individual level12, it is not known whether the impact of punishment similarly affects network dynamics related to cooperation. In an individual-level analysis of the data investigated here12, researchers found that contributions are significantly higher in a version of the game in which punishments are low-cost and high-impact. One interpretation of this result is that social norms about cooperation are most effectively developed when the cost-to-impact ratio is low. Second, the experimental networks investigated here are composed of a more representative sample12 than those that have been previously analyzed for cascades of cooperation27, which have investigated only college students. This is important not only for generalizability, but also because the expectation that participants did not know one another or have a sense of group identity prior to the experiment is nearly certain. This is important for understanding the effect of network relationships when the likelihood of pre-existing shared norms or beliefs about the actions of others that are tied to the known attributes of other game players is low, unlike when participants are known to be students at the same university (see the Supplementary Information for more discussion of the differences between the game setup in the two sets of experiments).

To study how the impact of punishment affects social influence in cooperative behavior, I analyze data from previously published public goods experiments in which the costs and impact of punishment varied12. Participants were arranged into groups of three and began each round of the experiment with an endowment of 20 monetary units (MU). Participants then were tasked with deciding if they would contribute to the group project, and if so how much of their endowment to contribute (between 0 and 20 MU). The total number of MU contributed to the group project was multiplied by 1.5 and split evenly to the group members. In the version of the game with no punishment the round would end at this point. There were four versions of the game with punishment, with varying costs and impact of punishment associated with each. In the versions of the game with punishment, participants were then given the option to pay a personal cost to reduce the MU a group member has. The punishment costs and impact varied across versions of the game. In the low-cost, low-impact version, punishment cost 1 MU and reduced the income of the target by 1 MU. In the high-cost, low-impact version, punishment cost 3 MU and reduced the income of the target by 1 MU. In the low-cost, high-impact version, punishment cost 1 MU and reduced the income of the target by 3 MU. In the high-cost, high-impact version, punishment cost 3 MU and reduced the income of the target by 3 MU.

Crucially for the present study, the design of the experiments ensured that participants were strictly anonymous from one another and never played a round of the game with another participant more than once. Participants played six rounds of the experiment, each with a new group of other participants with whom they had not yet interacted. These steps are frequently taken in such experiments to distinguish cooperative behavior from other processes, such as reciprocity15,39 and reputation40. This experimental design enables the experiment to be analyzed as a network in which the group members a participant plays with may influence a player in a subsequent round27. That is, as players move through the rounds of the experiment they become tied to other players, both directly and indirectly, through their own interaction history and the interaction history of those they have interacted with. For example, if participant A plays with participants B and C in round 1, in the subsequent round participants B and C are the first-degree alters of participant A. If participants B and C had contributed a high amount in round 1 we might expect that participant A would be more likely to contribute a high amount in round 2, having observed the contributions of participants B and C previously. If in the second round participant A plays with participants D and E, in the next round participants B and C would be the second-degree alters of participants D and E through participant A. As the rounds progress the network builds and more distant alters (further in social network terms) may influence the behavior of their group members through their decisions in the game.