Strategic interaction and imitation dynamic 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. Each area is characterized by a different fishing policy: an imposed constant fishing effort in a patch and oligopolistic competition in the other one, where fishermen are free to decide their harvesting on the basis of “boundedly rational” choices. Moreover, given the total number of fishermen, we propose an evolutionary approach, namely an adaptive switching, 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 past profits. The aim of this work is to fully specify the four-dimensional discrete time model, whose complete analysis will be carried out in a future paper. [email protected] University of Urbino Via A. Saffi 42, Urbino, Italy. [email protected] University of Calabria Via P. Bucci 3C, Rende (CS), Italy. [email protected] University of Urbino Via A. Saffi 42, Urbino, Italy. AMS references: 91A40, 91A80, 91B76.