In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where their network topologies change by continuous removal and addition of nodes. Each of these removal and addition can be either random or intentional. We therefore have four different strategies in changing network topology: random removal and random addition (RR), random removal and preferential addition (RP), targeted removal and random addition (TR), and targeted removal and preferential addition (TP). We find that cooperation clusters are the most fragile against TR, while they are the most robust against RP even in high temptation coefficients for defect. The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology due to consequential removal and addition of nodes, which is quite different from the cases observed in static networks. Cooperation clusters become more robust as the number of links of the hubs occupied by cooperators increase. Our results indicate that a huge variety of individuals are needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.
Robustness of cooperation on scale-free networks under continuous topological change
Genki Ichinose, Yuto Tenguishi, Toshihiro Tanizawa