Modeling and Computation of Mean Field Equilibria in Producers' Game with Emission Permits Trading

TL;DR

This paper develops a mean field game model for large-scale producer behavior under emission permit trading, deriving coupled PDEs and proposing a numerical method to analyze equilibrium states and trading effects.

Contribution

It introduces a novel mean field game framework with a fitted finite volume method for solving coupled PDEs in emission permit trading scenarios.

Findings

Emission permit prices influence producers to lower emissions.

The numerical method effectively solves the coupled PDEs.

Higher permit costs lead to reduced emission levels.

Abstract

In this paper, we present a mean field game to model the production behaviors of a very large number of producers, whose carbon emissions are regulated by government. Especially, an emission permits trading scheme is considered in our model, in which each enterprise can trade its own permits flexibly. By means of the mean field equilibrium, we obtain a Hamilton-Jacobi-Bellman (HJB) equation coupled with a Kolmogorov equation, which are satisfied by the adjoint state and the density of producers (agents), respectively. Then, we propose a so-called fitted finite volume method to solve the HJB equation and the Kolmogorov equation. The efficiency and the usefulness of this method are illustrated by the numerical experiments. Under different conditions, the equilibrium states as well as the effects of the emission permits price are examined, which demonstrates that the emission permits trading scheme influences the producers' behaviors, that is, more populations would like to choose a lower rather than a higher emission level when the emission permits are expensive.