Strategic interaction and imitation dynamics in patch differentiated exploitation of fisheries

In this paper we propose a discrete-time dynamic model for studying the time evolution of fish stocks in an aquatic environment divided into two adjacent patches, one characterized by an imposed constant fishing effort and another one where fishermen are free to decide the quantity to harvest according to oligopolistic competition taking into account economic and biologic externalities. Given the total number of fishermen, we propose an evolutionary switching mechanism, based on imitation dynamics, that endogenously regulates the fraction of fishermen that, at each time period, decide to operate in one of the two regions on the basis of observed past profits. Numerical simulations provide some insights into the role of the main parameters. This model has been motivated by a project for the creation of a marine protected area (MPA) in the Adriatic sea.