Multi-population Mean Field Games with Multiple Major Players: Application to Carbon Emission Regulations

In this paper, we propose and study a mean field game model with multiple populations of minor players and multiple major players, motivated by applications to the regulation of carbon emissions. Each population of minor players represent a large group of electricity producers and each major player represents a regulator. We first characterize the minor players' equilibrium controls using forward-backward differential equations, and show existence and uniqueness of the minor players' equilibrium. We then express the major players' equilibrium controls through analytical formulas given the other players' controls. Finally, we provide a method to solve the Nash equilibrium between all the players, and we illustrate numerically the sensitivity of the model to its parameters.