Evolutionary Dynamics in a Group Population Structure with Barriers to Group Entry

The evolution of cooperation has been studied in many systems, from bacterial communities to human populations. It is well known that population structure is crucial to dynamics. For humans, group memberships are critical; we often interact with each other due to common group memberships. There exist network-based models to study human dynamics, but they generally do not allow for multiple group affiliations or incorporate barriers to group entry. We present a framework in which individuals interact through an evolutionary game with those who share their groups and update stochastically, with strategy and group memberships subject to evolutionary updating. We impose barriers to group entry based on group size. We find that with barriers, cooperation emerges, but it is most favored when we allow for the existence of "loners": a changing subset of individuals who spend a temporary "time-out" period not interacting with others. This work provides an analytical framework in which behavior in realistic population structures can be studied, and adds to a growing body of literature that recognizes the existence of loners as vital parts of systems.