In this talk, we discuss a mean-field game price formation

model. This model describes a large number of rational agents that can

trade a commodity with an exogenous supply. The price is determined by

a balance condition between supply and demand. We discuss the

well-posedness of the model, the uniqueness and regularity of the

price function. Then, we examine two explicit models - the

linear-quadratic problem and a model with finitely many agents. Time

permitting, we will examine the connections between this problem and

optimal transport with constraints.