Group selection and network reciprocity are two well-known mechanisms for cooperation. And while they have separately received ample attention for their ability to promote cooperation in social dilemmas, their joint effects in this regard are much less explored.

Here we propose a multilayer network model that takes into account that not only individuals are connected by means of networks, but that also groups can be connected in much the same way. The model thus couples together network reciprocity and group selection, and it allows us to study their joint effect on the evolution of cooperation.

We use the prisoner’s dilemma game as the paradigmatic social dilemma example, showing that the fine-tuning of evolution frequency and the imitation rate in the group network play key roles in determining the survival thresholds of cooperators.

We also explore the importance of deterministic and stochastic updating rules, showing that the former provides more options to further promote cooperation. We discuss the importance of our findings for cooperation in structured interactions among groups and in higher-order networks.

Z. Shi, W. Wie, M. Perc, B. Li, Z. Zheng, Coupling group selection and network reciprocity in social dilemmas through multilayer networks, Applied Mathematics and Computation 418 (2022) 126835.