Dynamic social networks promote cooperation in experiments with humans

Abstract

Human populations are both highly cooperative and highly organized. Human interactions are not random but rather are structured in social networks. Importantly, ties in these networks often are dynamic, changing in response to the behavior of one's social partners. This dynamic structure permits an important form of conditional action that has been explored theoretically but has received little empirical attention: People can respond to the cooperation and defection of those around them by making or breaking network links. Here, we present experimental evidence of the power of using strategic link formation and dissolution, and the network modification it entails, to stabilize cooperation in sizable groups. Our experiments explore large-scale cooperation, where subjects' cooperative actions are equally beneficial to all those with whom they interact. Consistent with previous research, we find that cooperation decays over time when social networks are shuffled randomly every round or are fixed across all rounds. We also find that, when networks are dynamic but are updated only infrequently, cooperation again fails. However, when subjects can update their network connections frequently, we see a qualitatively different outcome: Cooperation is maintained at a high level through network rewiring. Subjects preferentially break links with defectors and form new links with cooperators, creating an incentive to cooperate and leading to substantial changes in network structure. Our experiments confirm the predictions of a set of evolutionary game theoretic models and demonstrate the important role that dynamic social networks can play in supporting large-scale human cooperation.

Fig. 1.

(A) Dynamic social networks prevent the tragedy of the commons. The fraction of players choosing to cooperate is stable in fluid dynamic networks (blue) but declines over time in random networks (red), fixed networks (green), and viscous dynamic networks (yellow). Game length is stochastic and varies across sessions, with a constant 80% chance of a subsequent round. Although one might expect to see more cooperation in the viscous condition than in the static condition and more cooperation in the static condition than in the random condition, any differences in cooperation across these conditions are far from statistical significance (considering either all rounds or only rounds 7–11; P > 0.45 for all comparisons). (B) As predicted, there is greater variation in the number of connections in the rapidly updating fluid dynamic condition than in the other conditions. The fraction of individuals having each possible number of connections is shown by condition, across all sessions and rounds.

Fig. 2.

(A) In the fluid dynamic condition, connections between two cooperators (CC links) are much more likely to be maintained during rewiring than connections between a cooperator and a defector (CD/DC links) or between two defectors (DD links). Interestingly, CD/DC links also are significantly more stable than DD links (P = 0.009). Error bars indicate SEMs, clustered on subject and session. (B) In the fluid dynamic condition, cooperators come to have more connections on average than defectors.

Fig. 3.

(A) Subjects are more likely to make new links with players who cooperated in the previous round than with those who defected, and are more likely to break existing links with partners who defected than with partners who cooperated. (B) Subjects who defected in the previous last round are more likely to switch to cooperation if other players break links with them. Conversely, the breaking of links does not affect the behavior of cooperators. Interestingly, subjects’ cooperation is not affected by whether others made new links with them. Error bars indicate SEMs, clustered on subject and session. Data from the fluid dynamic condition is shown. C, cooperation; D, defection. See SI Appendix for further analysis.

Fig. 4.

Structure and strategy snapshots over time in two representative experimental sessions. Blue nodes represent cooperating subjects; red nodes represent defecting subjects. Individual connections are shown as gray lines. The network is arranged using a force-based algorithm where the edges act like springs, so that nodes in a more highly connected network are drawn more closely together. In addition, the nodes are sized according to their number of connections, and nodes with no connections are omitted. In the fluid dynamic condition, cooperation is stable, the network evolves from being relatively spare to being quite dense, and cooperators come to have more connections than defectors. In the fixed condition, conversely, cooperation declines, and subjects with many connections are mostly defectors. Note that the connections do not change in the static network although the visualization algorithm alters the position of the nodes.