The system for producing (and consuming) electrical energy is undergoing a profound transformation, driven by two factors whose impact will increase significantly in the coming decades. On the one hand, the growing share of intermittent sources (solar, wind) in the energy mix and, on the other hand, technological advances that will make it increasingly possible to control the use of electrical appliances in households. Adapting this intermittent production to consumption will be one of the main challenges of the energy transition in the coming decades. The aim of the two internships proposed will be to address this problem in a simplified setting where ``agents'' are both electricity producers and consumers and to study the coordination between the agents within a game theoretic approach. This will imply two tasks, each the subject of an internship: i) the construction and study of a Mean Field Game describing the behavior of the agents, and ii) to take the point of view of the ``central authority'', leading to a problem of ``game design'' .