Growth Model With Externalities for the Energy Transition

We introduce a novel mean‐field game model for multi‐sector economic growth in which a dynamically evolving externality, influenced by the collective action of countries, plays a central role. By integrating environmental considerations in classical growth models, the framework incorporates “common noise” to capture shared uncertainties about the externality variable. We establish the existence and uniqueness of a 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.