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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月19日

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  • Yiru Cai,
  • Haobo Qi,
  • Xifeng Su,
  • Yi Tan

摘要

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.