Mean Field Models to Regulate Carbon Emissions in Electricity Production

TL;DR

This paper employs mean field control and game models to analyze how electricity producers balance renewable and fossil fuel sources under a carbon tax, comparing competitive and cooperative scenarios and the influence of regulation.

Contribution

It introduces a novel application of mean field models to regulate carbon emissions in electricity production, including analysis of equilibrium states and regulatory impacts.

Findings

Unique solutions for producer behavior under different scenarios.

Numerical insights into Nash and social optima.

Impact of carbon tax regulation on producer strategies.

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. We first prove that both problems have a unique solution using forward-backward systems of stochastic differential 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.