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Controlling polluting firms: Nash and Stackelberg strategies

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  • Halkos, George
  • Papageorgiou, George

Abstract

In this paper we model the conflict between the group of polluting firms of a country and the social planer of the same country which attempts to control the volume of emissions generated during the production process. Both players of the game have their own control policies which are the rate of emissions on behalf the polluting firms and the rate of pollution control (e.g. abatement or taxation) on behalf the home country. The common state variable of the model is the number of the polluting firms, which is better to minimized through the country’s control policy, but beneficial to maximized on the polluters’ side. From the game theoretic point of view the model setup is very simple and belongs in to the special class of differential games also called state separable differential games. An important property for these games is that the open-loop Nash equilibrium coincides with the Markovian (closed-loop) equilibrium and in the case of hierarchical moves the analytical solutions are easy obtained. The game proposed here is analyzed for both types of equilibrium, i.e. Nash and Stackelberg. In the simultaneous move game (i.e. the Nash game) we find the equilibrium analytical expressions of the controls for both players as well as the steady state stock of the polluting firms. A sensitivity analysis of the crucial variables of the model takes place. In the hierarchical move game (i.e. the Stackelberg game) we find the equilibrium values of the controls as well as of the state variable. As a result a comparison between the two types of equilibrium for the game takes place. The analysis of the comparison reveals that the conflict is more intensive (since both controls have greater values) for the case in which the polluting firms play as the leader of the hierarchical move game.

Suggested Citation

  • Halkos, George & Papageorgiou, George, 2014. "Controlling polluting firms: Nash and Stackelberg strategies," MPRA Paper 58947, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:58947
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    References listed on IDEAS

    as
    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, September.
    2. Engelbert Dockner & Gustav Feichtinger, 1991. "On the optimality of limit cycles in dynamic economic systems," Journal of Economics, Springer, vol. 53(1), pages 31-50, February.
    3. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, February.
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    Cited by:

    1. Halkos, George & Papageorgiou, George, 2016. "Optimal abatement and taxation for internalizing externalities: A dynamic game with feedback strategies," MPRA Paper 74467, University Library of Munich, Germany.
    2. George E. Halkos & George J. Papageorgiou, 2021. "Some Results on the Control of Polluting Firms According to Dynamic Nash and Stackelberg Patterns," Economies, MDPI, Open Access Journal, vol. 9(2), pages 1-13, May.
    3. Halkos, George E. & Papageorgiou, George J., 2017. "A dynamic game with feedback strategies for internalizing externalities," Economic Analysis and Policy, Elsevier, vol. 55(C), pages 147-157.
    4. George, Halkos E. & George, Papageorgiou J. & Emmanuel, Halkos G. & John, Papageorgiou G., 2019. "Environmental regulation and economic cycles," Economic Analysis and Policy, Elsevier, vol. 64(C), pages 172-177.

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    More about this item

    Keywords

    Pollution control; Environmental Economics; Differential games.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • Q50 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - General
    • Q52 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Pollution Control Adoption and Costs; Distributional Effects; Employment Effects
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling

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