Threshold incentive mechanisms for the sustainable management of public resources.

Maintaining global ecological balance is inextricably linked to the effective governance of public resources. Previous studies have proposed the introduction of incentive mechanisms to mitigate the defection behavior within the scope of public resource management to facilitate sustainable utilization. However, these incentive strategies often present a considerable financial burden. Here, we first propose a two-threshold incentive scheme based on group state objectives, where the reward mechanism is triggered when the number of cooperators is below the threshold M, and the punishment mechanism is triggered when the number of cooperators is above the threshold Q. We further introduce an incentive mechanism by considering both resource and group thresholds, where incentives are implemented separately when the number of cooperators and the current quantity of resources meet thresholds. Our theoretical results reveal that introducing these two new mechanisms can effectively maintain cooperative behavior and sustainable resources while reducing management costs. However, if the initial resource level is low, the tragedy of the commons will still occur. It is recommended that the number of developers be reduced, the allocation be lowered, or the development simply suspended and the natural regeneration of resources be waited for.