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19-01-2022

# Mean Field Models to Regulate Carbon Emissions in Electricity Production

Authors: René Carmona, Gökçe Dayanıklı, Mathieu Laurière

Published in: Dynamic Games and Applications

## Abstract

The most serious threat to ecosystems is the global climate change fueled by the uncontrolled increase in carbon emissions. In this project, we use mean field control and mean field game models to analyze and inform the decisions of electricity producers on how much renewable sources of production ought to be used in the presence of a carbon tax. The trade-off between higher revenues from production and the negative externality of carbon emissions is quantified for each producer who needs to balance in real time reliance on reliable but polluting (fossil fuel) thermal power stations versus investing in and depending upon clean production from uncertain wind and solar technologies. We compare the impacts of these decisions in two different scenarios: (1) the producers are competitive and hopefully reach a Nash equilibrium; (2) they cooperate and reach a social optimum. In the model, the producers have both time dependent and independent controls. We first propose nonstandard forward–backward stochastic differential equation systems that characterize the Nash equilibrium and the social optimum. Then, we prove that both problems have a unique solution using these equations. We then illustrate with numerical experiments the producers’ behavior in each scenario. We further introduce and analyze the impact of a regulator in control of the carbon tax policy, and we study the resulting Stackelberg equilibrium with the field of producers.

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Appendix
Available only for authorised users
Footnotes
2
We note that this function satisfies the assumptions that are necessary for existence and uniqueness. The fact that $$p(\cdot )$$ is convex can be justified by the increasing unit costs that comes from the search of land that is large enough to construct the solar panels on. However, in the numerical application, we take the $$p_3$$ and $$\epsilon$$ small to have a function that is nearly “linear.”

4
In order to capture the resale value of solar panels, when the experiments are for 10 years the cost of solar panel decreased by 25% and when they are for 2 years, the cost is decreased by 50%.

11
For the minor player’s problem, we have been able to choose realistic parameters by using real life data as explained in Sect. 4.3. However, the parameters for the regulator’s cost depend on the type of the regulator we focus on. For example, a regulator can care about minimizing the pollution relatively more than the other objectives or the regulator’s main goal can be to maximize demand matching by the producers. Therefore, in the experiments, we focus on showing the effect of these different parameter choices on the decision of the regulator.

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Title
Mean Field Models to Regulate Carbon Emissions in Electricity Production
Authors
René Carmona
Gökçe Dayanıklı
Mathieu Laurière
Publication date
19-01-2022
Publisher
Springer US
Published in
Dynamic Games and Applications
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-021-00422-y