Today's smart grid faces many challenges due to the rapid evolution of generation, distribution, and storage means which enable users to produce, store, and sell energy back to the providers. Demand response management plays a key role in achieving the objective of balancing electricity supply and demand efficiently. It also helps leveling consumption during peak hours. To do so, this paper proposes a game theoretic model for the multiperiodic smart grid demand side management problem with shifted demand. The proposed model has two major sets of players: Homeowners and electricity providers. We develop a 0–1 mixed linear programming approach to compute the Nash equilibria of the proposed game. We analyze the structure of the Nash equilibria to maintain the viability of the smart grid infrastructure. We also discuss the order relations between the users and the providers utility coefficients. Finally, we conduct extensive experiments on smart grid demand response synthetic data with different size. The obtained results demonstrate the scalability of the proposed game model.