Electric vehicles and mean-field

This chapter introduces mean field games to capture the mutual interaction between a population and its individuals. Within this context, a new equilibrium concept called mean field equilibrium replaces the classical Nash equilibrium in game theory. In a mean field equilibrium each individual responds optimally to the population behavior. In other words, no individuals have incentives to deviate from their current strategies. This new way of modeling the interactions among members of large populations is used to study dynamic demand response management in electricity grids. Moreover, some generalizations of the classical idea of mean field games are introduced to embrace the situations in which the whole population can be divided into classes of members.