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

Abstract

This talk presents a model to understand why economic activity tends to cluster in some places (agglomeration) rather than spread out. The approach uses a “mean-field game” framework, where many forward-looking individuals decide where to work and live over time in a continuous geographical space. People make decisions based on wages, prices, and their expectations about the future, while also facing random individual shocks. Wages and prices depend on the overall distribution of people across locations and are determined using standard trade models. In this talk, Raouf will demonstrate that the underlying trade system has a well-defined and unique equilibrium and establish that a dynamic equilibrium also exists, where people’s migration and work decisions evolve over time. Finally, the talk highlights how expectations about the future and uncertainty influence these patterns. The key result is that forward-looking behavior tends to strengthen agglomeration, although it does not overturn the overall pattern that would occur if people made short-sighted (myopic) decisions.

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