Effects of updating rules on the coevolving prisoner's dilemma

We studied the effect of three strategy updating rules in coevolving prisoner's dilemma games where agents (nodes) can switch both the strategy and social partners. Under two node-based strategy updating rules, strategy updating occurs between a randomly chosen focal node and its randomly selected neighbour. The focal agent becomes the strategy recipient and may imitate the strategy of the neighbour according to the payoff difference, i.e. voter-model-like dynamics (VMLD), or becomes a strategy donor and thus may be imitated by the neighbour, i.e. invasion-process-like dynamics (IPLD). For edge-based updating rules, one edge is selected, and the roles of the two connected nodes (donor or recipient) are randomly decided, i.e. edge-based dynamics (EBD). A computer simulation shows that partner switching supports the evolution of cooperation under VMLD, which has been utilised in many studies on spatial evolutionary games, whereas cooperators often vanish under IPLD. The EBD results lie between these two processes. This difference is prominent among nodes with large degrees. In addition, partner switching induces a non-monotonic relationship between the fraction of cooperators and intensity of selection under VMLD and EBD, and a weak or strong selection supports cooperation. In contrast, only a strong selection supports cooperators under IPLD. Similar differences in the enhancement of cooperation are observed when games are played on static heterogeneous networks. Our results imply that the direction of imitation is quite important for understanding the evolutionary process of cooperation.