In this paper we consider a game-theoretic dynamic model describing the exploitation of a renewable source. Our model is based on a Cournot oligopoly game where n profit-maximizing players harvest fish and sell their catch on m markets. We assume that the players do not known the law governing the reproduction of the resource. Instead they use an adaptive updating scheme to forecast the future fish stock. We analyze the resulting dynamical system which describes how the fish population and the forecasts (expectations) of the players evolve over time. We provide results on the existence and local stability of steady states. We consider the set of initial conditions which give non-negative trajectories converging to an equilibrium and illustrate how this set can be characterized. We show how such sets may change as some structural parameters of our model are varied and how these changes can be explained. This paper extends existing results in the literature by showing that they also hold in our two-dimensional framework. Moreover, by using analytical and numerical methods, we provide some new results on global dynamics which show that such sets of initial conditions can have complicated topological structures, a situation which may be particularly troublesome for policymakers.
