Evolution of conditional cooperation in collective-risk social dilemma with repeated group interactions

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.