Growth model with externalities for energetic transition via MFG with common external variable
Published in Preprint submitted to Mathematical Finance, 2025
with P. Lavigne and X. Warin.
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 countries, plays a central role. Building on classical growth theories and integrating environmental considerations, the framework incorporates “common noise” to capture shared uncertainties among countries about the externality variable. We establish the existence and uniqueness of the mean-field game equilibrium by reformulating the equilibrium conditions as a Forward–Backward Stochastic Differential Equation via the stochastic maximum principle, first applying a contraction-mapping argument to guarantee a unique solution, then employing the concept of weak equilibria to prove existence under more general assumptions, and finally invoking a specific monotonicity regime to reaffirm uniqueness. We provide a numerical resolution for a specified model using a fixed-point approach combined with neural network approximations.
https://arxiv.org/abs/2501.11988