Quality versus quantity of social ties in experimental cooperative networks

Abstract Recent studies suggest that allowing individuals to choose their partners can help to maintain cooperation in human social networks; this behaviour can supplement behavioural reciprocity, whereby humans are influenced to cooperate by peer pressure. However, it is unknown how the rate of forming and breaking social ties affects our capacity to cooperate. Here we use a series of online experiments involving 1,529 unique participants embedded in 90 experimental networks, to show that there is a ‘Goldilocks’ effect of network dynamism on cooperation. When the rate of change in social ties is too low, subjects choose to have many ties, even if they attach to defectors. When the rate is too high, cooperators cannot detach from defectors as much as defectors re-attach and, hence, subjects resort to behavioural reciprocity and switch their behaviour to defection. Optimal levels of cooperation are achieved at intermediate levels of change in social ties. Introduction Recent theoretical attention has focused on the role that population structure might have in the emergence of cooperation1,2,3. This work suggests that cooperation can be maintained when individuals are situated within a social network, interacting repeatedly with their immediate neighbours. The expectation is that cooperators will form mutually reinforcing clusters, which helps them to outcompete defectors4,5,6. Yet, empirical work has found that static network structure has little, if any, effect on promoting cooperation7,8,9,10. In contrast, dynamic networks that allow individuals to adjust social ties are able to maintain cooperation8,11. One reason is that dynamic networks offer an additional method of responding to the past actions of others; not only can players reciprocate by strategically changing their own cooperation behaviour (thus collectively increasing or decreasing the overall levels of cooperation evinced in the group as a whole) but they can also change their network ties, engaging in ‘tie reciprocity’11,12. Agent-based simulations show that dynamic networks favour cooperation under a wider range of assumptions about costs and benefits than static networks do6,13. As a result, there is growing interest in studying the coevolutionary dynamics of strategic behaviours and tie formation6,14,15,16,17. In these evolutionary models, positive feedback effects can result from preferential partner choice, where cooperative individuals keep attracting new partnerships and defecting individuals lose ties. This kind of social selection pressure can reinforce cooperation in the network, as shown by these models. However, prior theoretical work offers conflicting predictions about how cooperation will vary with the rate at which social ties may be formed or broken (the ‘rewiring rate’). Some recent theoretical (and also empirical) work shows that when individuals are allowed to rewire their networks more frequently, they are more likely to maintain cooperation6,11,16,18, suggesting that more frequent rewiring is always better. However, other work17 suggests that too high a rewiring rate could compromise cooperation. The theorized reason is that, although very high turnover in ties helps cooperators to cut ties with defectors, it can also diminish the chance of converting such defectors into cooperators by social influence or learning19; moreover, a very high turnover rate can provide relatively more opportunities for defectors to re-attach to cooperators than for cooperators to detach from defectors. Here we test these competing theoretical predictions by leveraging new tools for running economic games and conducting experiments online20,21. We find that there is a ‘Goldilocks’ effect of network dynamism on cooperation. When the rate of change in social ties is too low, subjects choose to have many ties, even if they attach to defectors; and when the rate is too high, cooperators cannot detach from defectors as much as defectors re-attach, and so subjects indeed resort to behavioural reciprocity and switch their behaviour to defection. Optimal levels of cooperation are achieved at intermediate levels of change in social ties. Results Structure of online experiments There is burgeoning interest in using online tools to create virtual labs to evaluate human behaviour11,21,22,23. The advantages are many, including the ability to recruit large samples quickly and the ease of conducting many replicates of experimental treatments. Using novel software and recruiting subjects from around the world to a virtual lab via the online labour market Amazon Mechanical Turk24,25,26,27,28, we were able to conduct a series of experiments that spanned the whole range of possible rewiring rates. We recruited 1,529 unique participants who were randomly assigned to one of nine conditions in a series of 90 realizations of our dynamic network experiments. Each participant was initially assigned a location in a random social network and then given a choice: either cooperate or defect. Participants who cooperate pay 50 units for each network neighbour and each of their neighbours receive 100 units. Participants who defect pay 0 units and their neighbours receive 0 units (each subject’s final score accumulated over all rounds was converted into dollars at an exchange rate of $1=1,000 units.) Before making each decision, participants were shown their neighbours and (after the first round) the neighbours’ previous decisions. They were only allowed to use the same strategy (cooperation or defection) simultaneously with all neighbours; this feature, of course, makes it harder to maintain cooperation because participants are more likely to use a conditional strategy and switch to defection29. At the end of each turn, participants were informed about the decisions of their neighbours in that round, along with their own payoff. These interactions were repeated for 15 rounds; to prevent final-round effects, we did not inform participants how many rounds would be played. Individuals were not allowed to participate in the experiment more than once (see Methods and Supplementary Fig. S1). Before each run of the experiment, we created a random social network with each possible connection among participants being realized with probability 0.2. Thereafter, at each round, participants chose whether or not to cooperate, and a fixed percentage of participant pairs were chosen at random in which one individual in the pair (also chosen at random) was allowed to decide whether to form a new tie if one did not exist or to cut a tie if one did exist (this percentage is the ‘rewiring rate’). In all pairs, the deciding participant was informed of the other’s choice to cooperate or defect in the preceding round. At the end of every rewiring opportunity, each participant was told the number of others who chose to break links with him or her and the number of others who formed new links with him or her. This being said, both the formation (...truncated)