Here, we examine a fully-discrete Semi-Lagrangian scheme for a mean-field game price formation model. We show that the discretization is monotone as a multivalued operator and prove the uniqueness of the discretized solution. 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. This scheme performs substantially better than standard methods by giving reliable results within a few iterations, as several numerical simulations and comparisons at the end of the paper illustrate.

翻译：本文研究了一种针对平均场博弈价格形成模型的全离散半拉格朗日格式。我们证明了该离散格式作为一个多值算子是单调的，并验证了离散解的唯一性。此外，利用单调性方法，证明了离散格式的极限收敛于连续价格形成平均场博弈的弱解。如文末若干数值模拟与对比所示，该格式在数次迭代内即可给出可靠结果，其性能显著优于标准方法。