A mean-field game model of price formation with price-dependent agent behavior

We propose a linear–quadratic mean-field game (MFG) model to study market price formation. We derive ordinary differential equations that predict the relation between the price and the demand and present various examples to show the implications of these equations on price formation through supply–demand equilibrium. While MFGs generally have a forward–backward structure, here, we exploit our problem’s structure to reduce it to initial value problems. We also discuss how the model parameters can be calibrated with statistical data.