  Here, we study machine learning (ML) architectures to solve a mean-field
games (MFGs) system arising in price formation models. We formulate a training
process that relies on a min-max characterization of the optimal control and
price variables. Our main theoretical contribution is the development of a
posteriori estimates as a tool to evaluate the convergence of the training
process. We illustrate our results with numerical experiments for linear
dynamics and both quadratic and non-quadratic models.
