  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 that are connected to the highest-degree
individuals, i.e., on networks 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 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.
