Punishment in bipartite societies.

๐Ÿ“… 2026-02-01
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๐Ÿค– AI Summary
In bipartite societies where group identity and strategic behavior are equally salient, conventional homogeneous punishment mechanisms struggle to foster cooperation effectively. This study proposes a bipartite public goods game model incorporating cross-group punishment directed exclusively at defectors from the opposing group. By integrating evolutionary game theory with group-level dynamic simulations, the research systematically examines how symmetric and asymmetric cross-group punishment influence the evolution of cooperation. The findings reveal that symmetric cross-group punishment significantly outperforms uniform punishment under conditions of low penalty intensity and small enhancement factors, thereby enhancing both cooperation levels and social welfare. In contrast, asymmetric punishment undermines the stability of cooperative behavior. These results demonstrate that symmetry is a critical principle for cross-group punishment to promote cooperation, thereby transcending the limitations of prior research confined to homogeneous group settings.

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๐Ÿ“ Abstract
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.
Problem

Research questions and friction points this paper is trying to address.

bipartite societies
intergroup punishment
cooperation
evolutionary dynamics
public goods game
Innovation

Methods, ideas, or system contributions that make the work stand out.

bipartite populations
intergroup punishment
symmetry
cooperation evolution
public goods game
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Sinan Feng
School of Mathematics and Statistics, Northwestern Polytechnical University, Xiโ€™an, 710072, Shaanxi, China; Shaanxi Provincial Key Laboratory of Intelligent Game Theory and Information Processing at Higher Education Institutions, Xiโ€™an, 710072, China
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Genjiu Xu
School of Mathematics and Statistics, Northwestern Polytechnical University, Xiโ€™an, 710072, Shaanxi, China; Shenzhen Research Institute, Northwestern Polytechnical University, Shenzhen, 518057, Guangdong, China
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Yu Chen
School of Mathematics and Statistics, Northwestern Polytechnical University, Xiโ€™an, 710072, Shaanxi, China; Shaanxi Provincial Key Laboratory of Intelligent Game Theory and Information Processing at Higher Education Institutions, Xiโ€™an, 710072, China
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Chaoqian Wang
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
Attila Szolnoki
Attila Szolnoki
Scientific Adviser, Institute of Materials Science and Technical Physics, Budapest
evolutionary game theorystatistical physics