Convergence of one-dimensional stationary mean field games with vanishing potential

Yiru Cai (), Haobo Qi (), Xifeng Su () and Yi Tan ()
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Yiru Cai: Beijing Normal University
Haobo Qi: Beijing Normal University
Xifeng Su: Beijing Normal University
Yi Tan: Beijing Normal University

Partial Differential Equations and Applications, 2025, vol. 6, issue 2, 1-16

Abstract: Abstract We consider the one-dimensional stationary first-order mean-field game (MFG) system with the coupling between the Hamilton–Jacobi equation and the transport equation. In both cases that the coupling is strictly increasing and decreasing with respect to the density of the population, we show that when the potential vanishes the regular solution of MFG system converges to the one of the corresponding integrable MFG system where the population is evenly distributed. Furthermore, we obtain the convergence rate of the above limit.

Keywords: Mean field games; Stationary problems; Regular solutions; Vanishing potential; Convergence rate; 91A13; 91A25; 47A55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00319-0

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