  The evolution and long-term sustenance of cooperation has consistently piqued
scholarly interest across the disciplines of evolutionary biology and social
sciences. Previous theoretical and experimental studies on collective risk
social dilemma games have revealed that the risk of collective failure will
affect the evolution of cooperation. In the real world individuals usually
adjust their decisions based on environmental factors such as risk intensity
and cooperation level. However, it is still not well understood how such
conditional behaviors affect the evolution of cooperation in repeated group
interactions scenario from a theoretical perspective. Here, we construct an
evolutionary game model with repeated interactions, in which defectors decide
whether to cooperate in subsequent rounds of the game based on whether the risk
exceeds their tolerance threshold and whether the number of cooperators exceeds
the collective goal in the early rounds of the game. We find that the
introduction of conditional cooperation strategy can effectively promote the
emergence of cooperation, especially when the risk is low. In addition, the
risk threshold significantly affects the evolutionary outcomes, with a high
risk promoting the emergence of cooperation. Importantly, when the risk of
failure to reach collective goals exceeds a certain threshold, the timely
transition from a defective strategy to a cooperative strategy by conditional
cooperators is beneficial for maintaining high-level cooperation.
