Effects of updating rules on the coevolving prisoner’s dilemma

Abstract

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. votermodel-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.

Hidden order behind the cooperation

“…The research of evolutionary game on the contact network mainly focuses on the following aspects: the influence of the differential network topology [28,29], some possible dynamic mechanisms that support the emergence of cooperative behavior [30][31][32], the co-evolution of network topology and game dynamics (i.e., the co-evolution of individual strategy and network topology) [33][34][35]. In this letter, we make an overview of evolutionary game research on complex networks, and put forward our prospective researches.…”

Symmetry breaking in the prisoner's dilemma on two-layer dynamic multiplex networks

“…During strategy updating, agents may imitate their neighbor's strategy in a specific layer. In such an event, one layer (λ) and one link in that layer (e (λ) i,j ) are randomly selected; one of the connected agents is randomly selected to become a focal agent, while the other becomes a role agent [52,75]. In the explanation provided here, agent i becomes a focal agent while agent j becomes a role agent.…”

Gradual learning supports cooperation in spatial prisoner’s dilemma game

“…The popularity of the latter protocol is based on the fact that not only biological systems but also human behavior can be modeled realistically by this rule [19,20,21]. One of the inspiring observations of previous studies was that the evolutionary outcome may depend sensitively on the applied microscopic dynamics [22,23,24,25,26,27,28].…”