Evolution of cooperation on scale-free networks subject to error and attack

TL;DR

This paper investigates how cooperation evolves on scale-free networks under random and targeted vertex removal, revealing high robustness to random errors but vulnerability to attacks on high-degree nodes, especially under high temptation to defect.

Contribution

It demonstrates the differential impact of random errors versus targeted attacks on cooperation in scale-free networks, highlighting the role of network heterogeneity in resilience.

Findings

Cooperation is highly robust against random vertex removal.

Targeted attacks on high-degree vertices rapidly diminish cooperation.

Network heterogeneity decrease correlates with loss of cooperation.

Abstract

We study the evolution of cooperation in the prisoner's dilemma and the snowdrift game on scale-free networks that are subjected to intentional and random removal of vertices. We show that, irrespective of the game type, cooperation on scale-free networks is extremely robust against random deletion of vertices, but declines fast if vertices with the maximal degree are targeted. In particular, attack tolerance is lowest if the temptation to defect is largest, whereby a small fraction of removed vertices suffices to decimate cooperators. The decline of cooperation can be directly linked to the decrease of heterogeneity of scale-free networks that sets in due to the removal of high degree vertices. We conclude that the evolution of cooperation is characterized by similar attack and error tolerance as was previously reported for information readiness and spread of viruses on scale-free networks.