Selection of Cooperation in Spatially Structured Populations

The social dilemma games give rise to an emergence of cooperation in which altruistic individuals survive the natural selection at higher rate than random chance. We try to extend our understanding of this spatial reciprocity by including the impact of degree-degree correlation on the propensity toward prosocial behaviour in an otherwise well-mixed population. In a stochastic death-birth process with weak selection, we find that the disassortative degree mixing, or negative correlation between the degrees of neighbouring nodes significantly promotes the fixation of cooperators whereas the assortative mixing acts to suppress it. This is consistent with the fact that the spatial heterogeneity weakens the average tendency of a population to cooperate, which we describe in a unified scheme of the effective isothermality in coarse-grained networks. We also discuss the individual-level incentives that indirectly foster restructuring the social networks toward the more cooperative topologies