The classic Vickrey-Clarke-Groves (VCG) mechanism ensures incentive compatibility, i.e., truth-telling is a dominant strategy for all agents, for a static one-shot game. However, it does not appear to be feasible to construct mechanisms that ensure dominance of dynamic truth-telling for agents comprised of general stochastic dynamic systems. The agents' intertemporal net utilities depend on future controls and payments, and a direct extension of the VCG mechanism does not guarantee incentive compatibility. This article shows that such a stochastic dynamic extension does exist for the special case of linear-quadratic-Gaussian (LQG) agents. In fact, it achieves subgame perfect dominance of truth-telling. This is accomplished through a construction of a sequence of layered payments over time that decouples the intertemporal effect of current bids on future net utilities if system parameters are known and agents are rational. An important motivating example arises in power systems where an independent system operator has to ensure balance of generation and consumption at all times, while ensuring social efficiency, i.e., maximization of the sum of the utilities of all agents. It is also necessary to satisfy budget balance and individual rationality. However, in general, even for static one-shot games, there is no mechanism that simultaneous satisfies these requirements while being incentive compatible and socially efficient. For a power market of LQG agents, we show that there is a modified "Scaled" VCG (SVCG) mechanism that does satisfy incentive compatibility, social efficiency, budget balance, and individual rationality under a certain "market power balance" condition where no agent is too negligible or too dominant. We further show that the SVCG payments converge to the Lagrange payments, defined as the payments that correspond to the true price in the absence of strategic considerations, as the number of agents in the market increases. For LQ but non-Gaussian agents, optimal social welfare over the class of linear control laws is achieved.