When Lasry-Lions meet Krugman: A mean-field game theory of spatial dynamics

M. Bahlali, Raouf Boucekkine () and Q. Petit
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M. Bahlali: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique
Q. Petit: EDF R&D

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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.

Keywords: Forward-looking behavior; Mean-field games; Spatiotemporal dynamics; Migrations; Trade (search for similar items in EconPapers)
Date: 2026-09
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Published in Journal of Economic Theory, 2026, 236, pp.106217. ⟨10.1016/j.jet.2026.106217⟩

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Journal Article: When Lasry-Lions meet Krugman: A mean-field game theory of spatial dynamics (2026)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05748104

DOI: 10.1016/j.jet.2026.106217

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