The role of the Allee effect in common pool resource games with environmental feedback

The management of common-pool resources harvested by multiple users is a complex and challenging collective action problem. In fact, self-interested users may aim for short-term individual rewards and decide to overuse the resource, thereby leading to its overexploitation or “tragedy of the commons”. The existence of shared goals within a community, however, has been shown to prevent overexploitation and favor the attainment of sustainable outcomes in coupled user decision-resource dynamics. Natural resource dynamics may exhibit a correlation between the size of the resource pool and its growth rate, a phenomenon known as “Allee effect”, which can induce a critical transition of the system to an over-depleted (‘unsustainable’) state if the resource harvest rate exceeds a critical level. In this study, we account for this non-linearity by incorporating the Allee effect in the common pool resource dynamics within a human-environment system accounting for both the impact of users' decisions on harvest rates and resource levels, and for the feedback of resource depletion on users' decision (i.e., the effect of resource-level knowledge on harvest rates). Our findings show that the Allee effect can induce bi-stability, whereby the system can converge to either a sustainable or unsustainable stable state, depending on initial conditions and parameter configurations. Furthermore, we demonstrate that incorporating knowledge feedback enhances system resilience and sustainability, offering insights into more effective CPR management strategies. These results underscore the importance of considering ecological and behavioral feedbacks in the management of shared resources and suggest that improving user awareness could significantly bolster sustainability efforts.