In smart grid, customers have access to the electricity consumption and the price data via smart meters; thus, they are able to participate in the demand response (DR) programs. In this paper, we address the interaction among multiple utility companies and multiple customers in smart grid by modeling the DR problem as two noncooperative games: the supplier and customer side games. In the first game, supply function bidding mechanism is employed to model the utility companies' profit maximization problem. In the proposed mechanism, the utility companies submit their bids to the data center, where the electricity price is computed and is sent to the customers. In the second game, the price anticipating customers determine optimal shiftable load profile to maximize their daily payoff. The existence and uniqueness of the Nash equilibrium in the mentioned games are studied and a computationally tractable distributed algorithm is designed to determine the equilibrium. Simulation results demonstrate the superior performance of the proposed DR method in increasing the utility companies' profit and customers' payoff, as well as in reducing the peak-to-average ratio in the aggregate load demand. Finally, the algorithm performance is compared with a DR method in the literature to demonstrate the similarities and differences.