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

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.

Keywords: Abel equation, Differential games, Non-linear feedback Nash equilibrium solution, Open-loop, Optimal management, Pollution control

Kossiorisa, G., M. Plexousakis, A. Xepapadeas, A. de Zeeuw, and K.-G. Mäler. 2008. Feedback Nash Equilibria for Non-linear Differential Games in Pollution Control. Journal of Economic Dynamics & Control 32:1312–1331.