Variable effort management of renewable natural resources

In this paper we introduce a resource management model of a common aquatic environment that is split into two regions: a protected area, where no harvesting is allowed, and an exploitable area, where a regulator imposes at each time period the maximum level of effort agents can exert. The imposed effort is not constant over time, but endogenously obtained through a negative feedback process according to the level of stock resource the regulator expects to prevail. Furthermore the fish population migrates within regions according to a linear diffusion mechanism. The results of the model can be easily adapted for different kinds of renewable stock resources management, such as water or air.