As a solution to the traditional electricity grid , smart grid is known as an organized interconnected structure of consumers , energy producers and energy transmitting systems that exchange information to enhance the smart energy system and keep it stable . smart energy production and supply grid requires a t argeted management as a new way to improve the quality of energy supply and reduce the cost of consuming electricity . In smart grid , demand side management is presented as a new method in this field , which uses smart measuring devices to analyze , evaluate and manage the consumption of users' shiftable loads . In autonomous demand side management , each consumer , as a subset of smart grid , uses grid information infrastructure to optimize its energy consumption in different time slots . This autonomous management of consumers requires optimization algorithms to achieve the optimal energy consumption in each time slot according to the behavior of other users on the grid . These optimization methods should have simple calculations and fast convergence rate so that they can be run at the processor and computing center of each consumer and in the shortest time this information should be transferred to other users or to the data collection center . In this research, a brief overview of smart grid and autonomous demand side management has been introduced and by modeling it using game theory the equilibrium points have been analyzed. In ADSM games, there is no guarantee for existance of Nash equilibriums and converging to them. If ADSM game can be modeled as a S-modular game, it will be easy to say about equilibrium points and convergence due to the properties of these games. Next , dual decomposition method and Lagrangian is considered as one of useful methods in modeling user consumption scheduling problems and also gradient projection method for solving these kinds of problems and finding equilibrium points in smart grid . The user scheduling problem is presented in two ways, one of them is considering users constraints regardless of grid constraints and the other one is considering both user and grid constraints. We have attempted to improve some of the algorithms presented in these field under the title of proposed algorithms . Finally, by simulating these algorithms their resault are numerically presented and their performances have been analysed and compared. Key Words : Autonomous Demand Side Management , Game Theory , Dual Decomposition Method , S-modular Game