A generalized Nash equilibrium for a bioeconomic problem of fishing

With the overexploitation of many conventional fish stocks, and growing interest in harvesting new kinds of food from the sea, there is an increasing need for managers of fisheries to take account of interactions among species. In this work we define a bioeconomic equilibrium model for ’n’ fishermen who catch three species; these species compete with each other for space or food. The natural growth of each species is modeled using a logistic law. The objective of the work is to find the fishing effort that maximizes the profit of each fisherman constrained by the conservation of the biodiversity. The existence of the steady states and its stability are studied using eigenvalue analysis. The problem of determining the equilibrium point that maximizes the profit of each fisherman is then solved by using the generalized Nash equilibrium problem. Finally, some numerical simulations are given to illustrate the results. key words: Bioeconomic model; Species in competition; Fishing effort; Maximizing profits for each fisherman; Generalized Nash Equilibrium GNE; Linear Complementarity Problem LCP; Biodiversity of renewable resources. Studia Informatica Universalis., pages 186 à 204 Nash equilibrium of fishing 187