Machine Learning architectures for price formation models

TL;DR

This paper explores machine learning architectures to solve mean-field game systems in price formation models, introducing a training process with convergence estimates and demonstrating results through numerical experiments.

Contribution

It develops a posteriori estimates for evaluating convergence in ML-based solutions to mean-field games in price models, a novel approach in this context.

Findings

Convergence estimates effectively evaluate training progress.

Numerical experiments validate the proposed ML architectures.

Applicable to linear and nonlinear price formation models.

Abstract

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.