We study the problem of charging an arbitrary number of plug-in electric vehicles (PEV) under a real-time electricity tariff that depends on the instantaneous grid load, with the addition of a stochastic process that affects the non-PEV demand. Each PEV is subjected to individual and coupling constraints. Formally, we are facing a Generalized Nash Equilibrium (GNE) seeking problem for stochastic aggregative games. The stochastic dynamics is modelized as an event tree and included according to the S-adapted information structure, which is suitable to describe stochastic processes that are independent of the players’ control. The equilibrium is calculated by employing a decentralized scheme. We observe that the valley-filling behavior, which has been observed in previous studies concerning the PEV problem, can be significantly altered by the stochastic dynamics.