The question of how cooperation evolves and is sustained over time has been a long-standing and unresolved issue in the fields of evolutionary biology and social sciences. Previous theoretical and experimental research based on the collective-risk social dilemma game has revealed the risk that the failure of collective goals will affect the evolution of cooperation. Considering that in the real world individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level, 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. Furthermore, our results confirm that a high risk can promote the emergence of cooperation. Importantly, when the risk exceeds the tolerance threshold, timely adjustment of strategies by conditional cooperators is beneficial for maintaining high-level cooperation.

We use MATLAB to numerically compute the evolutionary dynamics of the system.