In future smart grids, the electricity suppliers can modify the customers' load consumption pattern by implementing appropriate DSM (demand side management) programs using smart meters. Most of the existing studies on DSM, only consider one utility company in the supplier side. In this paper, the possibility of existing more than one supplier in the smart grid is addressed by modeling the DSM problem as two non-cooperative games: the supplier side game, and the customer side game. In the first game, the suppliers' profit maximization problem is formulated by applying supply function bidding mechanism. In the proposed mechanism, the electricity suppliers submit their bids to the DSM center, where the electricity price is computed and is sent to the customers. In the second game, the customers aim to determine optimal load profile to maximize their daily payoff. The existence and uniqueness of the Nash equilibrium in the mentioned games are explored and a computationally tractable distributed algorithm is designed to determine the equilibrium. Simulations are performed for a smart grid system with 3 suppliers and 1000 customers. Simulation results demonstrate the superior performance of the proposed mechanism in reducing the peak load and increasing the suppliers' profit and the customers' payoff. (C) 2015 Elsevier Ltd. All rights reserved.