Abstract
The present paper considers a dynamic nonzero-sum game between drug dealers and the authorities. Although the game is neither linear-quadratic nor degenerate, in the sense that the closed-loop equilibria coincide with the open-loop equilibria, we are able to calculate explicitly a stationary feedback Nash equilibrium of that game. In a numerical example, we determine the optimal allocation of governmental efforts between treatment and law enforcement minimizing the total discounted cost stream in the equilibrium. Moreover, we provide sensitivity analyses with respect to the efficiency parameters of both competitors. Our results show that a farsighted authority should attack the drug problem from the demand side and put much effort in treatment measures and the improvement of the efficiency of the treatment.
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Communicated by G. Leitmann
This research was supported by the Austrian Science Foundation under Contract P9112-SOZ. We would like to thank A. Luhmer and E. J. Dockner for helpful comments.
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Dawid, H., Feichtinger, G. Optimal allocation of drug control efforts: A differential game analysis. J Optim Theory Appl 91, 279–297 (1996). https://doi.org/10.1007/BF02190097
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DOI: https://doi.org/10.1007/BF02190097