  Here, we introduce a price-formation model where a large number of small
players can store and trade electricity. Our model is a constrained mean-field
game (MFG) where the price is a Lagrange multiplier for the supply vs. demand
balance condition. We establish the existence of a unique solution using a
fixed-point argument. In particular, we show that the price is well-defined and
it is a Lipschitz function of time. Then, we study linear-quadratic models that
can be solved explicitly and compare our model with real data.
