Alleviating collective action failure through dynamic targets and adaptive punishment in collective-risk dilemmas

The question of how to mitigate collective action failure has persistently drawn significant attention from researchers. However, previous theoretical and experimental studies have predominantly assumed a static target, thereby overlooking its inherent dynamic variability. To address this gap, we propose a two-stage three-party collective-risk social dilemma model: in the first stage, punishers sanction defectors; if the first-stage target is achieved, then the collective target is elevated in the second stage to sustain cooperation and mitigate greater risks, whereas failure triggers increased punishment intensity. We find that even in low-risk scenarios, the dynamic target and punishment mechanism can facilitate the emergence of high-level cooperation. Furthermore, moderate target elevation promotes cooperation, while excessive increases trigger cooperation collapse. At high risk, cooperation correlates positively with collective target size. Increasing first-stage punishment intensity within a suitable range boosts cooperation, with the effect more pronounced in low-risk scenarios.