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<p>Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that the limit of the discretization converges to the weak solution of the continuous price formation mean-field game using monotonicity methods. Numerical simulations demonstrate that this scheme can provide results efficiently, comparing favorably with other methods in the examples we tested.</p>

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A Fully-Discrete Semi-Lagrangian Scheme for a Price Formation MFG Model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月1日

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  • Yuri Ashrafyan,
  • Diogo Gomes

摘要

Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show the existence of the solution of the discretized problem and that it is monotone as a multivalued operator. Moreover, we show that the limit of the discretization converges to the weak solution of the continuous price formation mean-field game using monotonicity methods. Numerical simulations demonstrate that this scheme can provide results efficiently, comparing favorably with other methods in the examples we tested.