A Fully-discrete Semi-Lagrangian scheme for a price formation MFG model

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.