  Free-riding on a joint venture bears the risk of losing personal endowment as
the group may fail to reach the collective target due to insufficient
contributions. A collective-risk social dilemma emerges, which we here study in
the realm of the spatial public goods game with group-performance-dependent
risk levels. Instead of using an overall fixed value, we update the risk level
in each group based on the difference between the actual contributions and the
declared target. A single parameter interpolates between a step-like risk
function and virtual irrelevance of the group's performance in averting the
failure, thus bridging the two extremes constituting maximal and minimal
feedback. We show that stronger feedback between group performance and risk
level is in general more favorable for the successful evolution of public
cooperation, yet only if the collective target to be reached is moderate.
Paradoxically, if the goals are overambitious, intermediate feedback strengths
yield optimal conditions for cooperation. This can be explained by the
propagation of players that employ identical strategies but experience
different individual success while trying to cope with the collective-risk
social dilemma.
