Impact of link deletions on public cooperation in scale-free networks

¹ College of Physics and Technology, Guangxi Normal University - Guilin, Guangxi, China
² School of Electrical, Computer and Energy Engineering, Arizona State University - Tempe, AZ, USA
³ Department of Modern Physics, University of Science and Technology of China - Hefei, China
⁴ Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor - Maribor, Slovenia, EU
⁵ Department of Physics, Arizona State University - Tempe, AZ, USA
⁶ Research Center for Complex System Science, University of Shanghai for Science and Technology - Shanghai, China
⁷ Shanghai Academy of System Science - Shanghai, China

^a jiangluoluo@gmail.com

Received: 10 October 2010
Accepted: 24 January 2011

Abstract

Working together in groups may be beneficial if compared to isolated efforts. Yet this is true only if all group members contribute to the success. If not, group efforts may act detrimentally on the fitness of their members. Here we study the evolution of cooperation in public-goods games on scale-free networks that are subject to deletion of links connected to the highest-degree individuals, i.e., on network that are under attack. We focus on the case where all groups a player belongs to are considered for the determination of payoffs; the so-called multi-group public-goods games. We find that the effect of link deletions on the evolution of cooperation is predominantly detrimental, although there exist regions of the multiplication factor where the existence of an “optimal” number of removed links for the deterioration of cooperation can also be demonstrated. The findings are explained by means of wealth distributions and analytical approximations, confirming that socially diverse states are crucial for the successful evolution of cooperation.