An auction-based game is formulated for coordinating the charging of a population of electric vehicles (EVs) over a finite horizon. The proposed auction requires individual EVs to submit bid profiles that have dimension equal to two times the number of time-steps in the horizon. They compete for energy allocation at each time-step. Use of the progressive second price (PSP) auction mechanism ensures that incentive compatibility holds for the auction game. However, due to cross-elasticity between the charging time-steps, the marginal valuation of an individual EV at a particular time is determined by both the demand at that time and the total demand over the entire horizon. This difficulty is addressed by partitioning the allowable set of bid profiles according to the total desired energy over the entire horizon. It is shown that the efficient bid profile over the charging horizon is a Nash equilibrium of the underlying auction game. A dynamic update mechanism for the auction game is designed. A numerical example demonstrates that the auction system converges to the efficient Nash equilibrium.
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