  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.
