A Random-Supply Mean Field Game Price Model

Abstract

We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading costs, the market clears, and supply meets demand. This problem arises in market economies, including electricity generation from renewable sources in smart grids. Our model includes noise on the supply side, which is counterbalanced on the consumption side by storing energy or reducing the demand according to a dynamic price process. By solving a constrained minimization problem, we prove that the Lagrange multiplier corresponding to the market-clearing condition defines the solution of the price formation problem. For the linearquadratic structure, we characterize the price process of a continuum population using optimal control techniques. We include numerical schemes for the price computation in the finite and infinite games, and we illustrate the model using real data.

A Fully-discrete Semi-Lagrangian scheme for a price formation MFG model

“…Price problems with a stochastic supply and price were introduced in [14] and [15], respectively. Substantial effort was made to address the issue of common noise with machine learning (ML) techniques.…”

“…In [13], an ML approach employing dual recurrent neural networks and adversarial training to address the price formation MFG model with common noise is given. An ML training process was developed based on a min-max characterization of control and price variables in [12]. Using the potential transformation, [4] solved the price problem with common noise using a recurrent neural network.…”