Learning how to regulate a polluter with unknown characteristics: An application of genetic algorithms to a game of dynamic pollution control

  • Thomas Vallée
  • Christophe Deissenberg
Part of the Advances in Computational Management Science book series (AICM, volume 1)


We consider, within the framework of a dynamic game, the problem of a regulator using taxes to force a polluting monopolist to act in a socially optimal way. Traditionally it has been assumed that, in such a case, the regulator will implement his Stackelberg solution. However, the Stackelberg solution presupposes that the regulator knows exactly all characteristics of the monopolist. We show here that the on-line use of a genetic algorithm may allow the regulator to approximate the Stackelberg solution, even when he has only extremely limited information about the monopolist. While the results presented here are still preliminary, the fast convergence towards the analytic solution appears to suggest that the approach may be of practical value in real situations.


Genetic Algorithm Reaction Function Dynamic Game Stackelberg Game Pollution Stock 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Basar T. and Olsder G., Dynamic Noncooperative Game Theory New York: Academic Press, 2nd edition, 1995.Google Scholar
  2. Batabyal A., Consistency and optimality in a dynamic game of pollution control I: Competition, Economic Research Institute Study Paper, ERI 95–29, Utah State University, 1995.Google Scholar
  3. Batabyal A., Consistency and optimality in a dynamic game of pollution control II: Monopoly, Environmental and Resource Economics, 1996, 8: 315–330.CrossRefGoogle Scholar
  4. Carraro C. and Topa G., « Taxation and Environmental Innovation ». In Control and Game-Theoretic Models of Environment - Volume 2, Carraro C. and Filar J. eds., Birkhäuser, 1995.Google Scholar
  5. Holland J.H., Adaptation In Natural And Artificial Systems,University of Michigan Press, 1975.Google Scholar
  6. Goldberg D., Genetic Algorithm In Search, Optimization And Machine Learning,New York: Addison-Wesley, 1989.Google Scholar
  7. Pethig R., Conflicts and Cooperation in Managing Environmental Resources,Springer-Verlag, 1992.Google Scholar
  8. Vallée T. and Basar T., Off-line computation of the Stackelberg solutions with the Genetic Algorithm, submitted, Computational Economics, 1997.Google Scholar
  9. Vallée T., Deissenberg C. and Basar T., Optimal open-loop cheating in dynamic reversed linear quadratic Stackelberg games, forthcoming, Annals of Operations Research, 1997.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Thomas Vallée
    • 1
  • Christophe Deissenberg
    • 1
  1. 1.LEN-C3E Faculté des Sciences Economiques et de GestionUniversité de NantesFrance

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