  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.
