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

Modèle de croissance avec externalités pour la transition énergétique via MFG avec variable externe commune

Pierre Lavigne (), Quentin Petit () and Xavier Warin ()
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Pierre Lavigne: UniCA - Université Côte d'Azur
Quentin Petit: EDF - EDF
Xavier Warin: EDF - EDF

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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.

Keywords: Mean field games; Common noise; Growth models; Externality (search for similar items in EconPapers)
Date: 2025-01-20
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