  We define and analyze the notion of variational Wardrop equilibrium for
nonatomic aggregative games with an infinity of players types. These equilibria
are characterized through an infinite-dimensional variational inequality. We
show, under monotonicity conditions, a convergence theorem enables to
approximate such an equilibrium with arbitrary precision. To this end, we
introduce a sequence of nonatomic games with a finite number of players types,
which approximates the initial game. We show the existence of a symmetric
Wardrop equilibrium in each of these games. We prove that those symmetric
equilibria converge to an equilibrium of the infinite game, and that they can
be computed as solutions of finite-dimensional variational inequalities. The
model is illustrated through an example from smart grids: the description of a
large population of electricity consumers by a parametric distribution gives a
nonatomic game with an infinity of different players types, with actions
subject to coupling constraints.
