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Optimal control of interacting systems with DNSS property: The case of illicit drug use

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  • Zeiler, I.
  • Caulkins, J.P.
  • Tragler, G.

Abstract

Abstract 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.

Suggested Citation

  • Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 60-73, April.
  • Handle: RePEc:eee:jeborg:v:78:y:2011:i:1-2:p:60-73
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    References listed on IDEAS

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    1. 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.
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    5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    6. 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.
    7. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, April.
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    9. 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.
    10. 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.
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    Cited by:

    1. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2013. "When to make proprietary software open source," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1182-1194.

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