The Potential Method For Price-Formation Models

TL;DR

This paper introduces a potential function approach to mean-field game price formation models, transforming them into convex variational problems suitable for machine learning, and demonstrates this with neural network solutions and comparisons to analytical results.

Contribution

The paper presents a novel potential function formulation for MFG price models, enabling convex optimization and machine learning applications.

Findings

Convex variational formulation of the MFG model

Neural network solutions match analytical results

Framework facilitates machine learning approaches for price formation

Abstract

We consider the mean-field game price formation model introduced by Gomes and Sa\'ude. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and future prices. The balance between supply and demand determines the price. We introduce a potential function that converts the MFG into a convex variational problem. This variational formulation is particularly suitable for machine learning approaches. Here, we use a recurrent neural network to solve this problem. In the last section of the paper, we compare our results with known analytical solutions.