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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- Erdlenbruch, Katrin & Jean-Marie, Alain & Moreaux, Michel & Tidball, Mabel, 2010.
"Optimality of Impulse Harvesting Policies,"
IDEI Working Papers
603, Institut d'Économie Industrielle (IDEI), Toulouse.
- Katrin Erdlenbruch & Alain Jean-Marie & Michel MOREAUX & Mabel Tidball, 2010. "Optimality of Impulse Harvesting Policies," LERNA Working Papers 10.09.315, LERNA, University of Toulouse.
- Erdlenbruch, Katrin & Jean-Marie, Alain & Moreaux, Michel & Tidball, Mabel, 2010. "Optimality of Impulse Harvesting Policies," TSE Working Papers 09-150, Toulouse School of Economics (TSE).
- Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2010. "Optimality of Impulse Harvesting Policies," Working Papers hal-00864187, HAL.
- Mäler, K-G. & Xepapadeas, A. & Zeeuw, A.J. de, 2003.
"The economics of shallow lakes,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-123314, Tilburg University.
- Kiseleva, T. & Wagener, F.O.O., 2009.
"Bifurcations of optimal vector fields in the shallow lake model,"
CeNDEF Working Papers
09-12, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
- Michel, P., 1980.
"On the Transversality Condition in Infinite Horizon Optimal Problems,"
Cahiers de recherche
8024, Universite de Montreal, Departement de sciences economiques.
- Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-85, July.
- Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
- Polasky, Stephen & de Zeeuw, Aart & Wagener, Florian, 2011.
"Optimal management with potential regime shifts,"
Journal of Environmental Economics and Management,
Elsevier, vol. 62(2), pages 229-240, September.
- Stephen Polasky & Aart de Zeeuw & Florian Wagener, 2010. "Optimal Management with Potential Regime Shifts," CESifo Working Paper Series 3237, CESifo Group Munich.
- Stephen Polasky & Aart de Zeeuw & Florian Wagener, 2010. "Optimal Management with Potential Regime Shifts," Tinbergen Institute Discussion Papers 10-111/1, Tinbergen Institute.
- De Zeeuw, A. & Polasky, S. & Wagener, F.O.O., 2010. "Optimal Management with Potential Regime Shifts," CeNDEF Working Papers 10-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- W.A. Brock & D. Starrett, 2003. "Managing Systems with Non-convex Positive Feedback," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December.
- Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
- Rod Cross, 2000. "Hysteresis and Emu," Metroeconomica, Wiley Blackwell, vol. 51(4), pages 367-379, November.
- Michael Kopel & Herbert Dawid, 1999. "On optimal cycles in dynamic programming models with convex return function," Economic Theory, Springer, vol. 13(2), pages 309-327.
- Naevdal, Eric, 2006. "Dynamic optimisation in the presence of threshold effects when the location of the threshold is uncertain - with an application to a possible disintegration of the Western Antarctic Ice Sheet," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1131-1158, July.
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