The evolution of cooperation on structured population

In recent studies, it has been shown that cooperation can been improved when the population of selfish players is located on a heterogenous network. However, the theoretical analysis for the enhancement of cooperation on a heterogenous network is still short. In this work, we first model a heterogenous network by three simple networks with increasing complexity on their network structures. Then according to a master equation we develop the replication equations for the evolution of cooperation on these networks. The explicit formulations for the cooperator frequency on these networks are deduced and the relationship between the cooperator frequency and the network heterogeneity is discussed.