  In this article, we investigate the competitive interaction between
electrical vehicles or hybrid oil-electricity vehicles in a Cournot market
consisting of electricity transactions to or from an underlying electricity
distribution network. We provide a mean field game formulation for this
competition, and introduce the set of fundamental differential equations ruling
the behavior of the vehicles at the feedback Nash equilibrium, referred here to
as the mean field equilibrium. This framework allows for a consistent analysis
of the evolution of the price of electricity as well as of the instantaneous
electricity demand in the power grid. Simulations precisely quantify those
parameters and suggest that significant reduction of the daily electricity peak
demand can be achieved by appropriate electricity pricing.
