Network characteristics that facilitate the stable evolution of cooperation

In this paper we study the evolution of cooperation in the one-shot prisoner's dilemma in heterogeneous populations. Heterogeneity is defined by a contact network, which gives interaction partners and possibilities for strategy spreading in the population. We find that the high levels of cooperation previously reported for scale-free networks (SFNWs)(2-4) are unstable, when small probabilities for unmotivated strategy changes (mutations) are included in the evolution dynamics. Investigating the role of the network structure for the persistence and stability of cooperation, we use an optimization technique to generate small networks that allow a large fraction of cooperators to prosper. Analyzing these networks three key characteristics are identified: (i) degree heterogeneity, (ii) a set of hubs characterized by many connections to very low degree nodes, and (iii) a relatively large link density between these hub nodes. These findings motivate the introduction of a class of periphery-core networks, on which complete cooperation can evolve over the entire range of game parameters. On these networks cooperation also overwhelmingly dominates, even when relatively large mutation probabilities are included.