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On a strategic model of pollution control


  • Giorgio Ferrari

    () (Bielefeld University)

  • Torben Koch

    () (Bielefeld University)


This paper proposes a strategic model of pollution control. A firm, representative of the productive sector of a country, aims at maximizing its profits by expanding its production. Assuming that the output of production is proportional to the level of pollutants’ emissions, the firm increases the level of pollution. The government of the country aims at minimizing the social costs due to the pollution, and introduces regulatory constraints on the emissions’ level, which then effectively cap the output of production. Supposing that the firm and the government face both proportional and fixed costs in order to adopt their policies, we model the previous problem as a stochastic impulse two-person nonzero-sum game. The state variable of the game is the level of the output of production which evolves as a general linearly controlled one-dimensional Itô-diffusion. Following an educated guess, we first construct a pair of candidate equilibrium policies and of corresponding equilibrium values, and we then provide a set of sufficient conditions under which they indeed realize an equilibrium. Our results are complemented by a numerical study when the (uncontrolled) output of production evolves as a geometric Brownian motion, and the firm’s operating profit and the government’s running cost functions are of power type. An analysis of the dependency of the equilibrium policies and values on the model parameters yields interesting new behaviors that we explain as a consequence of the strategic interaction between the firm and the government.

Suggested Citation

  • Giorgio Ferrari & Torben Koch, 2019. "On a strategic model of pollution control," Annals of Operations Research, Springer, vol. 275(2), pages 297-319, April.
  • Handle: RePEc:spr:annopr:v:275:y:2019:i:2:d:10.1007_s10479-018-2935-7
    DOI: 10.1007/s10479-018-2935-7

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    References listed on IDEAS

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    More about this item


    Pollution; Stochastic impulse nonzero-sum game; Verification theorem; Diffusions;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • Q52 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Pollution Control Adoption and Costs; Distributional Effects; Employment Effects


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