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Some Results on the Control of Polluting Firms According to Dynamic Nash and Stackelberg Patterns

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  • George E. Halkos

    (Laboratory of Operations Research, Department of Economics, University of Thessaly, 38333 Volos, Greece)

  • George J. Papageorgiou

    (Laboratory of Operations Research, Department of Economics, University of Thessaly, 38333 Volos, Greece)

Abstract

In this paper we model the conflict between the group of polluting firms in a country and any social planner in the same country who attempts to control the volume of emissions generated during the production process. Both players of the game have their own control policies, i.e., the rate of emissions on behalf of the polluting firms and the rate of pollution control (e.g., pollution abatement or environmental taxation) on behalf of the home country. The common state variable of the model is the number of polluting firms, which aims to be minimized via the country’s control policy, but on the polluters’ side it is beneficial to be maximized. Regarding the game model, its setup belongs to the special class of differential games, which are called ‘state separable differential games’. An important property of these games is that the open-loop Nash equilibrium coincides with the Markovian (closed-loop) equilibrium and, in the case of hierarchical moves, analytical solutions are easily 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’s analytical expressions of the controls for both players, as well as the stationary value of the stock of polluting firms. A sensitivity analysis of the model’s crucial variables 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 act as the leader in the hierarchical move game.

Suggested Citation

  • George E. Halkos & George J. Papageorgiou, 2021. "Some Results on the Control of Polluting Firms According to Dynamic Nash and Stackelberg Patterns," Economies, MDPI, vol. 9(2), pages 1-13, May.
  • Handle: RePEc:gam:jecomi:v:9:y:2021:i:2:p:77-:d:556080
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    References listed on IDEAS

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    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. Halkos, George & Papageorgiou, George, 2014. "Controlling polluting firms: Nash and Stackelberg strategies," MPRA Paper 58947, University Library of Munich, Germany.
    3. Anna, Petrenko, 2016. "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(1), March.
    4. Gromova, Ekaterina V. & Tur, Anna V. & Balandina, Lidiya I., 2016. "A game-theoretic model of pollution control with asymmetric time horizons," Conference Papers 11933, Graduate School of Management, St. Petersburg State University.
    5. Peter Wood, 2010. "Climate Change and Game Theory," Environmental Economics Research Hub Research Reports 1062, Environmental Economics Research Hub, Crawford School of Public Policy, The Australian National University.
    6. 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, November.
    7. George Halkos, 1996. "Incomplete information in the acid rain game," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 23(2), pages 129-148, June.
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