  We study the evolution of cooperation in the collective-risk social dilemma
game, where the risk is determined by a collective target that must be reached
with individual contributions. All players initially receive endowments from
the available amount of common resources. While cooperators contribute part of
their endowment to the collective target, defectors do not. If the target is
not reached, the endowments of all players are lost. In our model, we introduce
a feedback between the amount of common resources and the contributions of
cooperators. We show that cooperation can be sustained only if the common
resources are preserved but never excessively abound. This, however, requires a
delicate balance between the amount of common resources that initially exist,
and the amount cooperators contribute to the collective target. Exceeding
critical thresholds in either of the two amounts leads to loss of cooperation,
and consequently to the depletion of common resources.
