Mean Field Models to Regulate Carbon Emissions in Electricity Production

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.