(Versión en español aquí)
In the very first post of this blog, I already introduced the idea of dynamic networks as a way out of the lack of experimental evidence on the promotion of cooperation by the structuring of the interactions (although recently an experiment has shown that there might be some such promotion when the temptation to defect is small, you should expect a post about this at some point soon). Recently, we set out to check exactly how this worked by looking at the effect of reputation, i.e., of the information given to experimental subjects about previous actions of their possible partners. This is described in our website Nectunt, under “Dynamic Networks and Reputation”, and has appeared a few weeks ago as Reputation drives cooperative behaviour and network formation in human groups, by José A. Cuesta, Carlos Gracia-Lázaro, Alfredo Ferrer, Yamir Moreno and Angel Sánchez, Scientific Reports 5, 7843 (2015). In a nutshell, what we found there is that the possibility to change links, by itself, does not promote cooperation; it has to be combined with information on the past actions of partners in order to induce a more cooperative behavior.
It is therefore very nice to report here a confirmation of this result, that has just appeared: The effects of reputational and social knowledge on cooperation, by Edoardo Gallo and Chang Yan, Proceedings of the National Academy of Sciences of the USA 112, 3647-3652 (2015). We knew about this work prior to publication, thanks to our common friend Antonio Cabrales who learned from Edo what they were doing and put us in contact, and we had a nice exchange of ideas. Later, I was external examiner of Chang’s Ph D Thesis at Oxford, which I enjoyed very much. Thus, it is a pleasure to talk about their work here.
Gallo and Yan started from the same setup we used, which, in fact, was nothing than the setup of Suri et al. A number of players, whom they recruited using the Amazon Mechanical Turk, forms a group in which they will interact by setting up or removing links with other players, and playing every round a Prisoner’s Dilemma game choosing the same action for all their present neighbors. I have to say that I am not a huge fan of using the Turk for economic experiments, but Gallo and Yan used it in a more appropriate manner than Suri et al., who allowed individuals to participate repeatedly in the experiment (one even took part in 78 games). They then conducted four treaments: in their own words,
In the baseline (B) treatment, subjects only have access to local reputational knowledge: a list of their current neighbors with the last five actions chosen by each one of them and a list of the nonneighbors without any information on their past actions. They also have access to local social knowledge only, so they have no information on the structure of the network beyond their neighbors. In the reputation (R) treatment, they have access to global reputational knowledge, so they see a list of the last five actions for every other subject, but they are still limited to local social knowledge. In the network (N) treatment, they have access to global social knowledge, so they see a network figure that shows the connections among all of the subjects in the group, but they only have access to local reputational knowledge. Finally, in the reputation and network (RN) treatment, they have access to global reputational and social knowledge by seeing the whole network and the last five actions for all other subjects.
The results show clearly the effect of the two types of intervention, reputation and network:
As panel A shows, unless there is information on how the possible partners behaved, i.e., reputation, cooperation is the same as in a static network, little. As soon as reputation enters the game, cooperation increases. In addition, with reputation participants make more money, the network they give rise to has more connections, and most people are connected with their neighbors’ neighbors. Interestingly, the network condition, i.e., the availability of global information on the social network with reputation restricted to knowledge about your first neighbors, does not affect any of these characteristics much. What is its effect then? To find out, let’s look into the network structure:
The figure shows examples of the networks formed under the four different treatments (left to right: baseline, network, reputation and both) at rounds 3, 7 and 11 (top to bottom). Nodes are indicated with circles whose size is proportional to their degree and whose cooperation in the last five rounds is given by their color according to the heat map indicated below. As Gallo and Yan say (actually, in their thorough and very informative supporting information),
The presence of both global reputation and global social knowledge in RN has no impact on the aggregate level of cooperation compared to R, but it has a distributional effect: it allows cooperators to fully exploit the ability to form and remove connections by creating a separate community which effectively excludes defectors. RN is the only treatment where there is a significant gap in outcomes depending on community membership: individuals in community C1 [the largest community] tend to be more cooperative than individuals in C2 [the second largest one] so C1 achieves a significantly higher cooperation level than C2, and within-community interactions produce a larger payoff for the community members of C1 compared to C2.
With their work, Gallo and Yan have shown a number of important points. First, in agreement with our previous work, the presence of global reputational knowledge is crucial for the emergence of a high level of cooperation, implying that the main driver of the results in previous experiments was the implicit assumption of the availability of global reputational knowledge. Second, knowledge on the social network as a whole affects the network formation process but not aggregate quantities such as cooperation level and relevante network metrics. And third, when both reputation and network information are available, this has an effect on how cooperative attitudes are distributed in the group. As the authors say, this may have an impact on our understanding of social networking tools and in particular on how they influence the emergence of communities whose members share (at least to some degree) a given behavior.