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The present paper describes a prey-predator type fishery model with two predators in competition. The aim of the paper is to maximize the net economic revenue earn from the fishery through implementing the sustainable properties of the fishery to keep the ecological balance. The existence of the steady states and the stability of the interior equilibrium point is studied using Routh Hurwitz criterion. The problem of determining the fishing effort that maximizes the net economic revenue of each fisherman results in a Generalized Nash Equilibrium Problem. More precisely, we are interested in equilibrium of mathematical game given by the situation where all fishermen try to optimize their strategies according to the strategies of all other fishermen. The importance of marine reserve is analyzed through the obtained results of the numerical simulations of proposed model system. The results depict that reserves will be most effective when the coefficient of catchability decreases.

Catchability coefficient influence on the fishermen's net economic revenues