The danger of collective failure permeates all levels of human society, making its mitigation critically important. Current theories often rely on a static collective target, which can be unrealistic or insufficient for fostering cooperation. This paper demonstrates a repeated game model featuring a dynamically adjusted governance strategy: if the stage target is met, the target for the next stage is increased; if not, the intensity of rewards for cooperators is enhanced. We find that adjusting collective targets is crucial for promoting cooperation. When risk is low, a moderately elevated target is effective; when risk is high, a higher target better sustains cooperation. Additionally, increasing rewards at low risk expands the basin of attraction for high cooperation, while at high risk it has little effect. This work establishes an effective adaptive governance framework for optimizing risk-sharing and maximizing cooperation, with broad application potential. Collective failure poses a significant challenge to sustaining cooperation in various systems. Here, the authors demonstrate that adaptively raising collective targets after success or increasing rewards after failure effectively maintains cooperation across different risk levels, offering a dynamic governance strategy with broad implications for enhancing collaborative efforts.
Xu et al. (Thu,) studied this question.