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

Mohamed Bahlali (), Raouf Boucekkine () and Quentin Petit ()
Additional contact information
Mohamed Bahlali: Aix-Marseille Univ., CNRS, AMSE, Marseille, France, https://www.amse-aixmarseille.fr/en/members/bahlali
Quentin Petit: EDF & FiME Lab, Paris, France

No 2517, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: We propose a mean-field game (MFG) set-up 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 twodimensional 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 Krugman (1996)'s racetrack economy, we obtain closed-form solutions for small sinusoidal 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.

Date: 2025-10
New Economics Papers: this item is included in nep-upt
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.amse-aixmarseille.fr/sites/default/fil ... rs/wp_2025_nr_17.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:2517

Access Statistics for this paper

More papers in AMSE Working Papers from Aix-Marseille School of Economics, France AMU-AMSE - 5-9 Boulevard Maurice Bourdet, CS 50498 - 13205 Marseille Cedex 1. Contact information at EDIRC.
Bibliographic data for series maintained by Gregory Cornu ().