Punishment in bipartite societies

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.