Dynamic problems of pollution and resource management with stock externalities often require a di¤erential games framework of analysis. In addition they are represented realistically by non linear transition equations. However, feedback Nash equilibrium (FBNE) 1 solutions, which are the desired ones in this case, are di¢ cult to obtain in problems with non linear-quadratic structure. We develop a method to obtain numerically non linear FBNE for a class of such problems, with a speci…c example for shallow lake pollution control.We compare FBNE solutions, by considering the entire equilibrium trajectories, with optimal management and open loop solutions and we show that the value of the best FBNE is in general worse than the open loop and optimal management solutions.

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