Evolution of cooperation through incomplete punishment under dynamic resource constraints

Institutional punishment plays an important role in promoting the evolution of cooperative behavior and has been widely studied. However, previous research has not adequately linked the sustainability of punishment resources to its effectiveness, as the dynamic interaction between resources and punitive actions remains poorly understood. Consequently, it remains unclear how the availability of punishment resources influences the punishment's effectiveness and, in turn, the evolution of cooperation. In reality, the availability of punishment resources is a prerequisite for implementing punishment. Based on this understanding, we extend the spatial public goods game with institutional punishment to simulate resource dynamics caused by identifying and punishing defectors. Simulation results reveal clear differences in how key parameters affect cooperation under sustainable versus unsustainable resource states. Notably, a high-fine and low-probability punishment strategy can both maintain resource sustainability and promote high levels of cooperation. Moreover, sequential screening facilitates the formation of large clusters of cooperators while preventing the expansion of defectors in spatial games. This punishment strategy and identification method offer theoretical insights for real-world social governance. Full punishment may not be the optimal strategy for institutions; instead, incomplete punishment is more efficient and common. This study provides a theoretical framework for exploring institutional punishment under resource constraints and deepens our understanding of how institutional punishment operates.