Evolution of prisoner's dilemma strategies on scale-free networks

Structural heterogeneity mediates the effect of community structure on cooperation

“…In the work by Chen [20] and current work, higher average connectivity k always results in lower density of cooperators. This result echoes some earlier findings based on various network models such as regular lattice [4], star structures [32], and scalefree networks [22], and so confirms that certain network structures promote cooperation and high connectivity reduces cooperation.…”

“…In the early works of evolutionary PDG on scale-free networks, the connectivity distribution of scale-free networks, which follows a power-law form and exhibits higher level of structural heterogeneity 1 than that of other networks (for example, regular lattices, small world networks, single-scale networks, and broad-scale networks), has been universally recognized as a key factor for cooperation in evolutionary PDG [14,15]. In recent years, there has been a gradually increasing attention to the effect of other structural properties (for example clustering, mixing pattern, and community structure) of scale-free networks on cooperation [20][21][22][23].…”

Heterogeneity of link weight and the evolution of cooperation

“…However, in a dilemma situation in the real world, we often see that altruistic behaviors exist among unrelated individuals. Nowak [6] proposed five rules as the mechanisms enabling the evolution of altruism: kin selection [7], direct reciprocity [4,8], indirect reciprocity [9,10], network reciprocity [11,12,13,14,15,16,17,18,19], and group selection [20].…”

“…That is, there is heterogeneity of the interactions among individuals. It has already been shown [13,14,15] that heterogeneity of interactions among individuals due to heterogeneity of the number of links among individuals and not to inter-individual heterogeneity can facilitate the evolution of cooperation. The literature [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] has investigated the effect of heterogeneity on the evolution of cooperation from variety of viewpoints 1 .…”

“…However, they investigated heterogeneity of interactions among individuals, which includes both intra-individual heterogeneity and interindividual heterogeneity, to the best of our knowledge. Inter-individual heterogeneity leads to heterogeneity of the link-weight amount, which causes heterogeneous interactions similar to those caused by the heterogeneity of the number of links, and the effect of the heterogeneity of the number of links on the promotion of cooperation has already been established in the literature[13,14,15].Therefore, the effect of link-weight heterogeneity on the evolution of cooperation may be given only by inter-individual heterogeneity whose effect is similar to that of the heterogeneity of the number of links. To investigate whether linkweight heterogeneity within each individual alone can promote cooperation, it is necessary to use a model with intra-individual heterogeneity and without interindividual heterogeneity.…”