From ant-acacia mutualism to performative conflict resolution among Inuit, dedicated punishments between distinct subsets of a population are widespread and can reshape the evolutionary trajectory of cooperation. Existing studies have focused on punishments within a homogeneous population, paying little attention to cooperative dynamics in a situation where belonging to a subset is equally important to the actual strategy represented by an actor. To fill this gap, we here study a bipartite population where cooperator agents in a public goods game penalize exclusively those defectors who belong to the alternative subset. We find that cooperation can emerge and remain stable under symmetric intergroup punishment. In particular, at low punishment intensity and at a small value of the enhancement factor of the dilemma game, intergroup punishment promotes cooperation more effectively than a uniformly applied punishment. Moreover, intergroup punishment in bipartite populations tends to be more favorable for overall social welfare. When this incentive is balanced, cooperators can collectively restrain defectors of the alternative set via aggregate interactions in a randomly formed working group, offering a more effective incentive. Conversely, breaking the symmetry of intergroup punishment inhibits cooperation, as the imbalance creates an Achilles' heel in the enforcement structure. Our work, thus, reveals symmetry in intergroup punishment as a unifying principle behind cooperation across human and biological systems.

翻译：从蚂蚁-金合欢互惠共生到因纽特人的表演性冲突解决，种群不同子集之间的专门惩罚广泛存在，并能重塑合作的演化轨迹。现有研究主要关注同质种群内的惩罚机制，鲜少探讨在个体所属子集身份与其实际行为策略同等重要的情境下的合作动力学。为填补这一空白，本研究考察了二分种群中公共物品博弈的合作者仅对属于另一子集的背叛者实施惩罚的情形。研究发现，在对称的群际惩罚机制下，合作能够涌现并保持稳定。具体而言，在低惩罚强度及低困境博弈增强因子的条件下，群际惩罚比统一实施的惩罚更能有效促进合作。此外，二分种群中的群际惩罚往往更有利于整体社会福利。当激励达到平衡时，合作者能通过随机形成的工作组中的聚合互动，集体制约另一子集的背叛者，从而提供更有效的激励。反之，打破群际惩罚的对称性会抑制合作，因为这种失衡会在执行结构中形成致命弱点。因此，本研究揭示了群际惩罚的对称性作为跨越人类与生物系统的合作现象背后的统一原则。