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

Author

Listed:
  • Yiru Cai

    (Beijing Normal University)

  • Haobo Qi

    (Beijing Normal University)

  • Xifeng Su

    (Beijing Normal University)

  • Yi Tan

    (Beijing Normal University)

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.

Suggested Citation

  • Yiru Cai & Haobo Qi & Xifeng Su & Yi Tan, 2025. "Convergence of one-dimensional stationary mean field games with vanishing potential," Partial Differential Equations and Applications, Springer, vol. 6(2), pages 1-16, April.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:2:d:10.1007_s42985-025-00319-0
    DOI: 10.1007/s42985-025-00319-0
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    References listed on IDEAS

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    1. P. Cardaliaguet, 2013. "Long Time Average of First Order Mean Field Games and Weak KAM Theory," Dynamic Games and Applications, Springer, vol. 3(4), pages 473-488, December.
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