Low-cost, high-impact altruistic punishment promotes cooperation cascades in human social networks

Theoretical models and experiments suggest that social networks may significantly impact the emergence and stability of cooperation in humans. Similarly, theoretical models and experiments have shown that punishing behavior can significantly increase cooperative behavior in individuals. However, how punishing impacts the effects of social networks on cooperation is not yet understood. Here, I examine a set of laboratory experiments in which participants choose to cooperate or defect under differing punishment arrangements. Through analysis of the experiment as a network, I evaluate how institutional arrangements affect the degree to which social networks promote cooperative behavior. The results show that cooperative behavior spreads from person-to-person in all versions of the game, but that in versions of the game with low-cost, high-impact punishment the influence both endures for more rounds and spreads further in the network. These results show that the extent to which cooperative behavior cascades is affected by the institutional arrangements that govern game play.


Introduction
shows the results of regression analysis of the effect of the first degree alter's contribution on the ego's contribution separately for the five versions of the public goods game. Table S2 shows the results of regression analysis of the effect of the second degree alter's contribution on the ego's contribution for the five versions of the public goods game. Table S3 shows the results of regression analysis of the effect of the third degree alter's contribution on the ego's contribution for the five versions of the public goods game. Table S4 shows the results of regression analysis of the effect of the fourth degree alter's contribution on the ego's contribution for the five versions of the public goods game. Table S5 shows the results of regression analysis of the effect of the first degree alter's contribution on the ego's contribution two rounds later for the five versions of the public goods game. Table S6 shows the results of regression analysis of the effect of the first degree alter's contribution on the ego's contribution three rounds later for the five versions of the public goods game. Table S7 shows the results of regression analysis of the effect of the first degree alter's contribution on the ego's contribution four rounds later for the five versions of the public goods game. Table S8 shows the results of regression analysis of the effect of the first degree alter's contribution on the ego's contribution five rounds later for the five versions of the public goods game. Table S9 shows the results of regression analysis of the mediation of the effect of the second degree alter's contribution on the ego's contribution by the first degree alter's contribution in the version of the public goods game with low-cost, high-impact punishment. Table S10 shows the results of regression analysis of the mediation of the effect of the second degree alter's contribution on the ego's contribution by the first degree alter's contribution in the version of the public goods game with high-cost, high-impact punishment. Table S11 shows the results of regression analysis of the effect of the average of first degree alter's contributions on contributions made by the ego in the next round in the five versions of the public goods game. Table S12 shows the results of regression analysis of the effect of the first degree alter's punishment given to the ego in the previous round on contributions made by the ego in the four versions of the public goods game with punishment. Table S13 shows the results of regression analysis of the effect of the average of first degree alter's punishments given to the ego in the previous round on contributions made by the ego in the four versions of the public goods game with punishment. Table S14 shows the results of regression analysis of the effect of the second degree alter's punishment received on contributions made by the ego two rounds later in the four versions of the public goods game with punishment. Table S15 shows the results of regression analysis of the effect of the first degree alter's punishment received on ego punishment given in the four versions of the public goods game with punishment. Table S16 shows the results of regression analysis of the interaction between punishment scenario and the first degree alter's contribution on ego contribution in the five versions of the public goods game. Table S17 shows the results of regression analysis of the interaction between punishment scenario and the second degree alter's contribution on ego contribution in the five versions of the public goods game. Table S18 shows the results of regression analysis of the interaction between punishment scenario and the third degree alter's contribution on ego contribution in the five versions of the public goods game. Table S19 shows the results of regression analysis of the interaction between punishment scenario and the fourth degree alter's contribution on ego contribution in the five versions of the public goods game. Table S20 shows the results of regression analysis of the interaction between punishment scenario and the first degree alter's contribution on ego contribution two rounds later in the five versions of the public goods game. Table S21 shows the results of regression analysis of the interaction between punishment scenario and the first degree alter's contribution on ego contribution three rounds later in the five versions of the public goods game. Table S22 shows the results of regression analysis of the interaction between punishment scenario and the first degree alter's contribution on ego contribution four rounds later in the five versions of the public goods game. Table S23 shows the results of regression analysis of the interaction between punishment scenario and the first degrees alter's contribution on ego contribution five rounds later in the five versions of the public goods game.
Although the experiments used by Fowler and Christakis (FC) [FC10] are similar to those examined here, the experimental procedures used differ from those conducted by Egas and Riedl (ER) [ER08] that are analyzed here. Of course, the most important difference is in the experimental conditions analyzed -FC [FC10] analyze only games in which there is either no punishment, or low-cost, high-impact punishment. I analyze five versions of the game, including the two analyzed by FC [FC10] and versions of the game with low-cost, low-impact punishment, high-cost, lowimpact punishment, and high-cost, high-impact punishment. The sample used by the two studies differ. All of the participants in the experiments analyzed by FC [FC10] are students, while the participants in the experiments conducted by ER [ER08] that I examine may be any adult who chose to participate. Relatedly, in the experiments analyzed by FC [FC10] the participants completed the study in a lab on campus, while the participants in the experimentsconducted by ER [ER08] that I analyze could complete the study in a setting of their choosing over the internet. Finally, in the experiments analyzed by FC [FC10] the groups in each round were of size four, while in the experimentsconducted by ER [ER08] that I examine the groups were of size three.
Although the models used below cluster on the ego and alter, it is possible that session-level factors account for some of the relationship between ego and alter contribution behavior. More specifically, it is possible that (after the first round) the data within a session become dependent in ways that the modeling strategy is not accounting for. One way of accounting for such dependencies would be to include a clusters on the session as well. However, there are only nine sessions in the data, which fall well short of recommendations of roughly 30-40 clusters. To test for the degree of dependency in the data, I conducted an intraclass correlation analysis for each of the models. To do so, I created predicted values for each participant using the model. Then, I calculated the intraclass correlation on the predicted values. High intraclass correlation values would indicate that group structure, or in this case session-level differences in behavior, was likely unaccounted for in the model. However, in none of the models did I find an intraclass correlation above 0.06. These results indicate that session-level variation is unlikely to account for the relationship between ego and alter contribution.

Public Goods
Public Goods Public Goods Public Goods Public Goods Game with Game with Game with Game with Game with no punishment low-cost, high-cost, low-cost, high-cost, low-impact low-impact high-impact high-impact punishment punishment punishment punishment Alter contribution t-1 0.14 (0.04) * * 0.11 ( Table S1: Tobit regression analysis of first-degree alter's contribution on ego's subsequent contribution. Tobit regression model of alter's contribution on ego's contribution in the next round, controlling for contribution by ego in a previous round and fixed effects for each round. To account for multiple observations of egos and alters, Huber-White sandwich errors are used clustering on each ego and alter.

Public Goods
Public Goods Public Goods Public Goods Public Goods Game with Game with Game with Game with Game with no punishment low-cost,  Table S2: Tobit regression of second-degree alter's contribution on ego's subsequent contribution. Tobit regression model of alter's alter's contribution on ego's contribution two rounds later, controlling for contribution by ego in two rounds previous and fixed effects for each round. To account for multiple observations of egos and alters, Huber-White sandwich errors are used clustering on each ego and alter.

Public Goods
Public Goods Public Goods Public Goods Public Goods Game with Game with Game with Game with Game with no punishment low-cost,                 Table S13: Tobit regression of average of first-degree alter's punishments of ego on ego's contribution in the subsequent round. Tobit regression model of average of alter's punishments given to ego on ego's contribution in the subsequent round, controlling for ego's and average of alter's contributions in the previous round, and fixed effects for each round. To account for multiple observations of egos, Huber-White sandwich errors are used clustering on each ego.

DV: Ego contribution in round t Public Goods Public Goods
Public Goods Public Goods Game with Game with Game with Game with low-cost, high-cost, low-cost, high-cost, low-impact low-impact high-impact high-impact punishment punishment punishment punishment Punishment received by Alter in Round t-2     Table S16: Tobit regression analysis of the interaction between punishment scenario and first-degree alter's contribution for the public goods game. Tobit regression models of alter's contribution on ego contribution interacted with low-cost, high-impact punishment condition (Model A) or interacted with all punishment scenarios separately (Model B), controlling for ego's and alter's contributions in the previous round, fixed effects for round and for cost and impact of punishment, using Huber-White sandwich errors to account for multiple observations of egos and alters. Data in these models are the pooled data across the five experimental procedures (no punishment, low-cost and low-impact punishment, low-cost and high-impact punishment, high-cost and low-impact punishment, high-cost and high-impact punishment).  Table S17: Tobit regression analysis of the interaction between punishment scenario and second-degree alter's contribution for the public goods game. Tobit regression models of alter's alter's contribution on ego contribution interacted with low-cost, high-impact punishment condition (Model A) or interacted with all punishment scenarios separately (Model B), controlling for ego's and alter's contributions in two rounds previous, fixed effects for round and for cost and impact of punishment, using Huber-White sandwich errors to account for multiple observations of egos and alters. Data in these models are the pooled data across the five experimental procedures (no punishment, low-cost and low-impact punishment, low-cost and high-impact punishment, highcost and low-impact punishment, high-cost and high-impact punishment).  Table S19: Tobit regression analysis of the interaction between punishment scenario and fourth-degree alter's contribution for the public goods game. Tobit regression models of alter's alter's alter's alter's contribution on ego contribution interacted with low-cost, highimpact punishment condition (Model A) or interacted with all punishment scenarios separately (Model B), controlling for ego's and alter's contributions in four rounds previous, fixed effects for round and for cost and impact of punishment, using Huber-White sandwich errors to account for multiple observations of egos and alters. Data in these models are the pooled data across the five experimental procedures (no punishment, low-cost and low-impact punishment, low-cost and high-impact punishment, high-cost and low-impact punishment, high-cost and high-impact punishment).