This paper studies the strategic behavior of firms competing in the exploitation of a common-access productive asset, in the presence of pollution externalities. We consider a differential game with two state variables (asset stock and pollution stock), and, by using a piecewise-linear approximation of the nonlinear asset growth function, we provide a tractable characterization of the symmetric feedback-Nash equilibrium, which is globally asymptotically stable. The results show that the firm's strategy takes three forms depending on the pair of state variables, and that different options for the model parameters lead to contrasting outcomes in both the short- and long-run equilibria.