Switching to a Green and sustainable finance setting: a mean field game approach

We consider a continuum of carbon-emitting firms who seek to maximise their stock price, and a regulator (e.g., Government) who wishes for the economy to flourish, whilst simultaneously punishing firms who behave non-green. Interpreting the regulator as a major player and the firms as the minor players, we model this setting through a mean field game with major and minor players. We extend the stochastic maximum principle derived by Carmona & Zhu [A probabilistic approach to mean field games with major and minor players. Annals of Applied Probability, 2016, 94, 745--788] by relaxing the assumptions on the forms of the minimisers for the Hamiltonians, allowing them to depend on more arguments. This allows the major and representative minor player to interact in a more natural fashion, thereby permitting us to consider more realistic models for our green and sustainable finance problem. Through our stochastic maximum principle, we derive explicit Nash equilibria for a number of examples.