A Dynamic Model for No-Take Marine Reserves

We consider an infinite time horizon discrete fishing game with a migratory species between three regions, (i) an open access fishing area with $N$ symmetric players, (ii) a marine protected area (MPA) with limited fishing activities that is accessible to only one player, (iii) and a fish bank area where fishing is completely prohibited. We analyze fishing strategies for different behaviors, i.e., a fully non-cooperative scheme, a social optimum and a cartel setting. We characterize the model equilibria and show, in terms of the environmental welfare of the resource, the positive impact that the introduction of the fish bank can exert on the level of the steady-state stocks in the three regions. This effect has a double benefit, that is the sustainability of the resource and an increase in income from the additional catching quantities over the time horizon for all fishers. We also show that these results may not be obtained under certain conditions. Our analytical results are supported by the use of a numerical simulation that compares different scenarios, including the current state of the world in contrast to different sizes of MPAs and fish bank areas