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.