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

TL;DR

This paper develops a mean field game model with multiple minor and major players to analyze carbon emission regulation, providing equilibrium characterizations and numerical insights into the model's sensitivity.

Contribution

It introduces a novel multi-population mean field game framework with multiple major players, offering analytical solutions and a method to compute Nash equilibria in the context of carbon regulation.

Findings

Existence and uniqueness of minor players' equilibrium controls.

Analytical formulas for major players' equilibrium controls.

Numerical analysis of model sensitivity to parameters.

Abstract

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 then provide a method to solve the Nash equilibrium between all the players, and we illustrate numerically the sensitivity of the model to its parameters.