In this paper, we consider a smart grid where users behave selfishly, aiming at minimizing cost in the presence of uncertain wind power availability. We adopt a demand side management (DSM) model, where active users (so-called prosumers) have both private generation and local storage availability. These prosumers participate to the DSM strategy by updating their energy schedule, seeking to minimize their local cost, given their local preferences and the global grid constraints. The energy price is defined as a function of the aggregate load and the wind power availability. We model the resulting problem as a non-cooperative Nash game and propose a semi-decentralized algorithm to compute an equilibrium. To cope with the uncertainty in the wind power, we adopt a rolling-horizon approach, and in addition we use a stochastic optimization technique. We generate several wind power production scenarios from a defined probability density function (PDF), determining an approximate stochastic cost function. Simulations results on a real dataset show that the proposed approach generates lower individual costs compared to a standard expected value approach.@en