Presentation on YouTube.

We propose a mean-field game (MFG) approach to study the dynamics of spatial agglomeration in a continuous space-time framework where trade across locations may follow a broad class of static gravity models. Forward-looking agents work and migrate in a two-dimensional geography and face idiosyncratic shocks. Equilibrium wages and prices depend on their common distribution and adjust statically according to the underlying trade model. We first prove the existence and uniqueness of the static trade equilibrium. We then prove the existence of dynamic equilibria. Finally, we apply our model to a simple circular geography to understand what the MFG theory can tell us about the forces driving agglomeration and dispersion in a dynamic setting. (with Raouf Boucekkine and Quentin Petit)