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D. Grass, A. Xepapadeas, A. de Zeeuw:
"Optimal Management of Ecosystem Services with Pollution Traps: The Lake Model Revisited.";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2017-03 (2017), 03; 43 pages.

In this paper, optimal management of the lake model and common property outcomes are reconsidered when the lake model is extended with a slowly changing variable (describing sedimentation and recycling of phosphorus), which is considered fixed in the simplified version that has been used in the literature up to now. Some intuitive results are reconfirmed but new optimal trajectories are found that were hidden in the simplified analysis. Moreover, it is shown that in the case of common-property, two Nash equilibria exist in a certain area of initial states where the one leading to the
steady state with a high level of ecological services dominates the other one.
However, for larger initial states, only the Nash equilibrium steady state with a low level of ecological services exists. This implies that at the separating states a significant drop in welfare occurs, and the users of the lake are trapped in the bad Nash equilibrium when this line is crossed (a pollution trap). Finally, it is shown what the consequences are of implementing the optimal phosphorus loadings from the simplified version into the full
lake model. The welfare losses can be considerable, and it can happen that the lake ends up in the wrong basin of attraction, but in most cases the welfare losses are small because of the fast-slow dynamics. The analytical tool that is used in this paper is an advanced extension of a Matlab solver for boundary value problems.

ecosystem services, lakes, multiple equilibria, pollution trap, optimal control, games, fast-slow dynamics

http://publik.tuwien.ac.at/files/publik_261857.pdf