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In this paper, we investigate a practical demand side management scenario where the selfish consumers compete to minimize their individual energy cost through scheduling their future energy consumption profiles. We adopt an instantaneous load billing scheme to effectively convince the consumers to shift their peak-time consumption and to fairly charge the consumers for their energy consumption. For the considered DSM scenario, an aggregative game is first formulated to model the strategic behaviors of the selfish consumers. By resorting to the variational inequality theory, we analyze the conditions for the existence and uniqueness of the Nash equilibrium (NE) of the formulated game. Subsequently, for the scenario where there is a central unit calculating and sending the real-time aggregated load to all consumers, we develop a one timescale distributed iterative proximal-point algorithm with provable convergence to achieve the NE of the formulated game. Finally, considering the alternative situation where the central unit does not exist, but the consumers are connected and they would like to share their estimated information with others, we present a distributed synchronous agreement-based algorithm and a distributed asynchronous gossip-based algorithm, by which the consumers can achieve the NE of the formulated game through exchanging information with their immediate neighbors.

Autonomous Demand Side Management Based on Energy Consumption Scheduling and Instantaneous Load Billing: An Aggregative Game Approach