Robustness of cooperation on scale-free networks under continuous topological change

TL;DR

This study examines how cooperation in prisoner's dilemma games on scale-free networks withstands continuous topological changes, revealing that the type of node removal and addition significantly impacts cooperation robustness.

Contribution

It introduces a comprehensive analysis of cooperation robustness under various dynamic network topologies, highlighting the influence of removal/addition strategies and degree distribution.

Findings

Cooperation is most fragile under targeted removal with random addition.

Preferential addition enhances cooperation robustness.

Degree mixing pattern has limited impact on cooperation stability.

Abstract

In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where the network topologies change by continuous removal and addition of nodes. Each 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 most fragile against TR, while they are most robust against RP, even for large values of the temptation coefficient for defection. 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, which is quite different from the cases observed in static networks. Cooperation clusters become more robust as the number of links of hubs occupied by cooperators increase. Our results might infer the fact that a huge variety of individuals is needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.