We study the existence and uniqueness of Nash equilibria for a certain class of aggregative games with finite and possibly large number of players. Sufficient conditions for these are obtained using the theory of variational inequalities together with the specific structure of the objective functions. We further present an algorithm that converges to the Nash equilibrium in a decentralized fashion with provable guarantees. The theoretical results are applied to the problem of managing the charging of a large fleet of plug-in electric vehicles and the results are compared with the existing work.