  We propose a machine learning method to solve a mean-field game price
formation model with common noise. This involves determining the price of a
commodity traded among rational agents subject to a market clearing condition
imposed by random supply, which presents additional challenges compared to the
deterministic counterpart. Our approach uses a dual recurrent neural network
architecture encoding noise dependence and a particle approximation of the
mean-field model with a single loss function optimized by adversarial training.
We provide a posteriori estimates for convergence and illustrate our method
through numerical experiments.
