A game theoretical approach to the vertical coexistence of small and big fish

Abstract

An abstract model of a pursuit-evasion game using tools from network economics is presented. Animal moves are represented as human migrations: people move to destinations that they find agreeable to migrate to and the associated decision-making depends on the specific characteristics of the location that they come from, the place that they migrate to, the distance between both, but also on the density and the characteristics of the other members of the human population living there. This competitive behavior results in a simple non-cooperative game. The repetition of this game, in turn, yields a dynamical system, the equilibrium of which may be computed using variational inequality tools. These ideas are implemented in the model of a vertical marine ecosystem in which big fish pursue small fish that try to evade, with the small fish preferring to live in surface and with the big fish preferring to reside in depth. The theoretical and computational results suggest that the specific trade-offs for both pursuers and evaders are important for the stability and the permanence of ecosystems. Then, we discuss how this quite simple model could be a first step toward a game theoretical formalization of the connectivity of marine ecosystems, which is an important and open question in marine ecology.