CMUC Mini-Course in Analysis - Diogo A. Gomes

September 2, 2024, at 2:00 PM. Room 2.4.

Title: Mean-Field Games: from price formation in commodity markets to monotonicity methods

Abstract: In the first part of this talk, we discuss the application of Mean-Field Game (MFG) theory to price formation. We introduce a constrained MFG model for price formation in commodity markets, such as electricity, where numerous small players engage in storage and trading. The price emerges as a Lagrange multiplier balancing supply and demand, and we prove its existence and uniqueness using fixed-point arguments.

Building upon this foundation, we propose a linear-quadratic MFG model to investigate market price formation further. We demonstrate how supply-demand equilibrium shapes price dynamics by deriving ordinary differential equations that predict the relationship between price and demand. Notably, we simplify the typically forward-backward structure of MFGs to initial value problems.

In the second part of the talk, we discuss monotone operator methods for MFGs. We present both a general regularization procedure and corresponding existence results. Then,  we address the uniqueness. We introduce a new linearization method and establish a weak-strong uniqueness result for stationary MFG systems.