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Journal Articles Journal of Dynamics and Games Year : 2021

A mean field game model for the evolution of cities

Abstract

We propose a (toy) MFG model for the evolution of residents and firms densities, coupled both by labour market equilibrium conditions and competition for land use (congestion). This results in a system of two Hamilton-Jacobi-Bellman and two Fokker-Planck equations with a new form of coupling related to optimal transport. This MFG has a convex potential which enables us to find weak solutions by a variational approach. In the case of quadratic Hamiltonians, the problem can be reformulated in Lagrangian terms and solved numerically by an IPFP/Sinkhorn-like scheme as in [4]. We present numerical results based on this approach, these simulations exhibit different behaviours with either agglomeration or segregation dominating depending on the initial conditions and parameters.
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Dates and versions

hal-03086616 , version 1 (22-12-2020)

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César Barilla, Guillaume Carlier, Jean-Michel Lasry. A mean field game model for the evolution of cities. Journal of Dynamics and Games, 2021, 8 (3), pp.299. ⟨10.3934/jdg.2021017⟩. ⟨hal-03086616⟩
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