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

• 成果类型: Article
• 署名作者: Bahlali, M.; Boucekkine, R.; Petit, Q.
• 署名单位: Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2026.106217
• 发表日期: 2026
• 关键词: general equilibrium-analysis; index theorem; TRADE; MODEL; mobility

摘要

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.