Research paper on Some Results on Dynamic Nash and Stackelberg Patterns-Based Control of Polluting Firms

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Title: Some Results on Dynamic Nash and Stackelberg Patterns-Based Control of Polluting Firms

Abstract: In this study, we model the conflict between a nation’s polluting businesses and any social planner attempting to limit the amount of emissions produced during the production process. Both players in the game have their own control strategies, i.e., the rate of emissions for the polluting companies and the rate of pollution control (for instance, pollution abatement or environmental taxation) for the home nation. The number of polluting businesses makes up the model’s common state variable. It is intended to be minimized through the nation’s control policy, but on the polluters’ side, maximization is advantageous. In terms of the game model, its configuration falls under the unique category of differential games known as “state separable differential games.” These games have two significant characteristics: the open-loop Nash equilibrium and the closed-loop Markovian equilibrium, and in the case of hierarchical moves, analytical solutions are simple to find. The game that is being proposed here is examined for both Nash and Stackelberg equilibria. We discover the analytical expressions of the controls for both players in the simultaneous move game (also known as the Nash game) as well as the stationary value of the stock of polluting firms. The critical parameters of the model are subjected to sensitivity analysis. We discover the equilibrium values of the controls and the state variable in the hierarchical move game (also known as the Stackelberg game). As a result, a comparison of the game’s two types of equilibrium is done. Since both controls have higher values, the comparison analysis shows that the conflict is more intense in the scenario where the polluting firms take the lead in the hierarchical move game.

Keywords: pollution control; environmental economics; differential games

Paper Quality: SCOPUS / Web of Science Level Research Paper

Subject: Economics

Writer Experience: 20+ Years

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