Optimal control of interacting systems with DNSS property: The case of illicit drug use
AbstractAbstract In this paper we generalize a one-dimensional optimal control problem with DNSS property to a two-dimensional optimal control problem. This is done by taking the direct product of the model with itself, i.e. we combine two similar system dynamics under a joint objective functional that is separable in both states and controls. This framework can be applied to the construction of various optimal control problems, such as optimal marketing of related products, optimal growth of separate but interacting economies, or optimal control of two related capital stocks. We study such a system for a particular case drawn from the domain of drug control. The main result of this paper is that in this domain even a modest amount of interaction can sometimes make a very big difference. Hence, drawing conclusions by simplifying the real world into two independent, one-dimensional models may be problematic. Methodologically the combination of two systems with DNSS property leads to a fascinating series of situations with multiple optimal steady states and associated threshold behavior. These instances reflect some important recent developments in optimal dynamic control theory.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Behavior & Organization.
Volume (Year): 78 (2011)
Issue (Month): 1-2 (April)
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Web page: http://www.elsevier.com/locate/jebo
Optimal control Indifference points Multiple equilibria DNSS points Illicit drug use Interacting systems;
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- Behrens, Doris A. & Caulkins, Jonathan P. & Tragler, Gernot & Feichtinger, Gustav, 2002. "Why present-oriented societies undergo cycles of drug epidemics," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 919-936, June.
- Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
- MÃ¤ler, K-G. & Xepapadeas, A. & Zeeuw, A.J. de, 2000.
"The Economics of Shallow Lakes,"
2000-69, Tilburg University, Center for Economic Research.
- Caulkins, Jonathan P. & Hartl, Richard F. & Kort, Peter M. & Feichtinger, Gustav, 2007.
"Explaining fashion cycles: Imitators chasing innovators in product space,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 31(5), pages 1535-1556, May.
- Caulkins, J.P. & Hartl, R.F. & Kort, P.M. & Feichtinger, G., 2007. "Explaining fashion cycles: Imitators chasing innovators in product space," Open Access publications from Tilburg University urn:nbn:nl:ui:12-194289, Tilburg University.
- 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.
- L‚onard,Daniel & Long,Ngo van, 1992.
"Optimal Control Theory and Static Optimization in Economics,"
Cambridge University Press, number 9780521337465.
- L‚onard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586.
- 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.
- Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
- Caulkins, Jonathan P. & Feichtinger, Gustav & Johnson, Michael & Tragler, Gernot & Yegorov, Yuri, 2005. "Skiba thresholds in a model of controlled migration," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 490-508, August.
- Feichtinger, Gustav & Grienauer, Waltraud & Tragler, Gernot, 2002. "Optimal dynamic law enforcement," European Journal of Operational Research, Elsevier, vol. 141(1), pages 58-69, August.
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