Growth model with externalities for energetic transition via MFG with common external variable

TL;DR

This paper develops a new mean-field game model for economic growth with a shared externality influenced by collective actions, incorporating environmental factors and uncertainties.

Contribution

It introduces a novel MFG framework with a common external variable, proving existence and uniqueness of equilibrium, and offers a neural network-based numerical solution.

Findings

Proved existence and uniqueness of the MFG equilibrium.

Reformulated equilibrium as a Forward-Backward SDE.

Implemented a neural network approach for numerical resolution.

Abstract

This article introduces a novel mean-field game model for multi-sector economic growth in which a dynamically evolving externality, influenced by the collective actions of agents, plays a central role. Building on classical growth theories and integrating environmental considerations, the framework incorporates common noise to capture shared uncertainties among agents about the externality variable. We demonstrate the existence and uniqueness of a strong mean-field game equilibrium by reformulating the equilibrium conditions as a Forward-Backward Stochastic Differential Equation under the stochastic maximum principle and establishing a contraction argument to ensure a unique solution. We provide a numerical resolution for a specified model using a fixed-point approach combined with neural network approximations.