Efficient demand side management through dynamic power pricing is an important application in the smart grids. However, in the absence of a detailed user consumption model, it is difficult to set an optimal power price. In this paper, we propose to efficiently capture the user consumption behavior through a user-dependent acceptance price. Each rational user will decide its own acceptance price based on its desire to get served. Then, we model the selfish interaction between operator and users as a Stackelberg game, where the operator aims to maximize its profit, while the individual users try to pay the lowest price and be served in time. After each user selfishly declares its own acceptance price, the operator sets an optimal power price, based on the user feedback and taking into account the random output of the renewable power sources. Simulation results confirm that the operator can maximize its profit and the users get served in time, while the proposed scheme leads to the optimal usage of the renewable power production.