Cooperation in large groups and one-shot interactions is often hindered by freeloading. Punishment can enforce cooperation, but it is usually regarded as wasteful because the costs of punishing offset its benefits. Here, we analyze an evolutionary game model that integrates upstream and downstream reciprocity with costly punishment: integrated strong reciprocity (ISR). We demonstrate that ISR admits a stable mixed equilibrium of ISR and unconditional defection (ALLD), and that costly punishment can become productive: When sufficiently efficient, it raises collective welfare above the no-punishment baseline. ALLD players persist as evolutionary shields, preventing invasion by unconditional cooperation (ALLC) or alternative conditional strategies (e.g., antisocial punishment). At the same time, the mixed equilibrium of ISR and ALLD remains robust under modest complexity costs that destabilize other symmetric cooperative systems.

翻译：大规模群体和单次互动中的合作常因搭便车行为而受阻。惩罚虽能强制执行合作，但通常被视为低效策略，因为惩罚成本会抵消其收益。本文提出一种整合上游与下游互惠机制的高成本惩罚演化博弈模型：整合性强互惠（ISR）。研究表明，ISR允许ISR与无条件背叛（ALLD）形成稳定的混合均衡态，且高成本惩罚可转化为高效策略：当惩罚效率足够高时，集体福利将超越无惩罚基准水平。ALLD参与者作为演化屏障持续存在，能有效抵御无条件合作（ALLC）或其他条件性策略（如反社会惩罚）的入侵。与此同时，在适度复杂性成本（足以破坏其他对称合作系统稳定性）的条件下，ISR与ALLD的混合均衡态仍保持稳健性。