A Minimal Model for the Emergence of Cooperation in Randomly Growing Networks

Cooperation is observed widely in nature and is thought an essential component of many evolutionary processes, yet the mechanisms by which it arises and persists are still unclear. Among several theories, network reciprocity — a model of inhomogeneous social interactions — has been proposed as an enabling mechanism to explain the emergence of cooperation. Existing evolutionary models of this mechanism have tended to focus on highly heterogeneous (scale-free) networks, hence typically assume preferential attachment mechanisms, and consequently the prerequisite that individuals have global network knowledge. Within an evolutionary game theoretic context, using the weak prisoner’s dilemma as a metaphor for cooperation, we present a minimal model which describes network growth by chronological random addition of new nodes, combined with regular attrition of less fit members of the population. Specifically our model does not require that agents have access to global information and does not assume scale-free network structure or a preferential attachment mechanism. Further our model supports the emergence of cooperation from initially non-cooperative populations. By reducing dependency on a number of assumptions, this model offers broad applicability and as such may support an explanation of the emergence of cooperation in early evolutionary transitions, where few assumptions can be made.