Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model
AbstractAbstract: In this article we analyze how the presence of thresholds influences multi agent decision making situations. We introduce a class of discounted autonomous optimal control problems with threshold effects and discuss tools to analyze these problems. Later, using these results we investigate two types of threshold effects; namely, simple and hysteresis switching, in the canonical model of the shallow lake. We solve the optimal management and open loop Nash equilibrium solutions for the shallow lake model with threshold effects. We establish a bifurcation analysis of the optimal vector field. Further, we observe that modeling with threshold effects simplifies this analysis. To be precise, the bifurcation scenarios rely on simple rules (inequalities) which can be verified easily. However, the qualitative behavior of the switching vector field is similar to the smooth case.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-001.
Date of creation: 2012
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Web page: http://center.uvt.nl
Optimal control; Differential games; Threshold effects; Discontinuous dynamics; Shallow lake;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics
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