When Lasry-Lions meet Krugman: A mean-field game theory of spatial dynamics
Abstract
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 intertemporal utility-maximizing 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 existence and uniqueness of the static trade equilibrium. We then prove existence of dynamic equilibria. In the case of a circular economy, we obtain closed-form solutions for small perturbations around the steady state, and we identify the sets of parameters that lead to agglomeration or dispersion. We exploit the MFG structure of the model to explicitly quantify how uncertainty and forward-looking expectations contribute to agglomeration and dispersion. In particular, we show that, regardless of the static trade model, forward-looking expectations always promote agglomeration, but cannot reverse the dominant pattern that would arise under myopic behavior.
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BibTeX
@article{bahlali2026when,
title = {{When Lasry-Lions meet Krugman: A mean-field game theory of spatial dynamics}},
author = {M. Bahlali and R. Boucekkine and Q. Petit},
journal = {Journal of Economic Theory},
year = {2026},
month = sep,
doi = {10.1016/j.jet.2026.106217},
url = {https://amu.hal.science/hal-05748104v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - When Lasry-Lions meet Krugman: A mean-field game theory of spatial dynamics
AU - M. Bahlali
AU - R. Boucekkine
AU - Q. Petit
PY - 2026
DA - 2026/09/13
JO - Journal of Economic Theory
DO - 10.1016/j.jet.2026.106217
UR - https://amu.hal.science/hal-05748104v1
AB - 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 intertemporal utility-maximizing 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 existence and uniqueness of the static trade equilibrium. We then prove existence of dynamic equilibria. In the case of a circular economy, we obtain closed-form solutions for small perturbations around the steady state, and we identify the sets of parameters that lead to agglomeration or dispersion. We exploit the MFG structure of the model to explicitly quantify how uncertainty and forward-looking expectations contribute to agglomeration and dispersion. In particular, we show that, regardless of the static trade model, forward-looking expectations always promote agglomeration, but cannot reverse the dominant pattern that would arise under myopic behavior.
SN - 0022-0531
SN - 1095-7235
ER -