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Feedback Nash Equilibria for Non-linear Differential Games in Pollution Control

G. Kossiorisa, M. Plexousakis, A. Xepapadeas, A. de Zeeuw, K.-G. Mäler. 2008 Journal of Economic Dynamics & Control, 32 (2008) 1312–1331, (2008).

Abstract:

Dynamic problems of pollution and resource management with stock externalities often require a differential games framework of analysis. In addition they are represented realistically by non-linear transition equations. However, feedback Nash equilibrium (FBNE) solutions, which are the desired ones in this case, are difficult to obtain in problems with nonlinear- quadratic structure. We develop a method to obtain numerically non-linear FBNE for a class of such problems, with a specific example for shallow lake pollution control. We compare FBNE solutions, by considering the entire equilibrium trajectories, with optimal managementand 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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Keywords: Differential games, Pollution control, Non-linear feedback Nash equilibrium solution, Abel equation, Open-loop, Optimal management

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