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 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.