| Abstract: |
| In this presentation, we propose a novel model for managing fisheries, described by a system of three coupled partial differential equations. The first is a reaction-diffusion equation representing the dynamics of the fish population, which follows standard approaches in the mathematical literature on spatial ecology. The other two equations are derived using a mean-field-game framework to model a large population of fishermen, where the number of fishermen is assumed to be large enough to be treated as infinite. Each fisherman aims to maximize their individual profit, calculated as the revenue from selling fish minus the cost of moving their boat. Under two different structural assumptions about the nonlinearities in the fish dynamics, we prove theoretical results illustrating the tragedy of the commons. Specifically, we show that a lack of coordination among fishermen can significantly harm, or even lead to the extinction of, the fish population. Our findings are supported by several numerical simulations. |
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