Sustainability of common-pool resources hinges on the interplay between human and environmental systems. However, there is still a lack of a novel and comprehensive framework for modelling extraction of common-pool resources and cooperation of human agents that can account for different factors that shape the system behavior and outcomes. In particular, we still lack a critical value for ensuring resource sustainability under different scenarios. In this paper, we present a novel framework for studying resource extraction and cooperation in human-environmental systems for common-pool resources. We explore how different factors, such as resource availability and conformity effect, influence the players' decisions and the resource outcomes. We identify critical values for ensuring resource sustainability under various scenarios. We demonstrate the observed phenomena are robust to the complexity and assumptions of the models and discuss implications of our study for policy and practice, as well as the limitations and directions for future research.