Evolutionary Reputation Games On Social Networks

We adapt an evolutionary model based on indirect reciprocity to the context of a structured population. We investigate the influence of clustering on the dynamics of cooperation in social networks exhibiting short average path length and various levels of locality. We show empirically how, as expected, a higher degree of locality, measured by clustering, can promote cooperation in a game involving reputation. More surprisingly, we show that a higher degree of locality results in slower convergence times for the population. These results show the existence of a trade-off between the need for higher cognitive abilities (understood as a longer memory of past interactions and/or the ability to keep tabs on a larger number of people) and the convergence time needed to reach a cooperative equilibrium. A population of individuals will need higher cognitive abilities to achieve a faster convergence time; on the other hand, a population with lower cognitive abilities may be able to reach the cooperative equilibrium but will get there slower. The trade-off between the rate of convergence and the need for higher cognitive abilities can be controlled by tuning the amount of locality in the graph (the clustering). These results shed some light on two facts: (1) Successful groups that do not rely on institutional enforcement of social norms tend to present a high degree of clustering; (2) Groups that experience rapid changes in membership tend to present low clustering.