While the classic Vickrey-Clarke-Groves mechanism ensures incentive compatibility for a static one-shot game, it does not appear to be feasible to construct a dominant truth-telling mechanism for agents that are stochastic dynamic systems. The contribution of this paper is to show that for a set of LQG agents a mechanism consisting of a sequence of layered payments over time decouples the intertemporal effect of current bids on future payoffs and ensures truth-telling of dynamic states by their agents, if system parameters are known and agents are rational. Additionally, it is shown that there is a "Scaled" VCG mechanism that simultaneously satisfies incentive compatibility, social efficiency, budget balance as well as individual rationality under a certain "market power balance" condition where no agent is too negligible or too dominant. A further desirable property is that the SVCG payments converge to the Lagrange payments, the payments corresponding 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 the optimal social welfare over the class of linear control laws is achieved.
A smart grid connects several electricity consumers producers, e.g., wind solar storage farms, fossil-fuel plants, industrial commercial loads, or load-serving aggregators, all modeled as stochastic dynamical systems. In each time period, each consumes supplies some electrical energy. Each such agent's utility is the benefit accrued from its consumption or the negative of its generation cost. The social welfare, the sum of all these utilities, is the total benefit accrued from all consumption minus the total cost of generation. The independent system operator is charged with maximizing the social welfare subject to total generation equalling consumption in each time period, but without the agents revealing their system states, dynamic models, utility functions, or uncertainties. It has to announce prices after interacting with agents via bid-price interactions. This paper examines the case where the agents respond in a compliant price-taking manner. It is shown that there is an iterative bid-price interaction, where agents respond to price announcements by complying to the requirement to announce their optimal responses according to their true stochastic model, or, in the case where the agents are linear quadratic Gaussian (LQG) systems, according to deterministic versions of their true stochastic models, that leads to the same global maximum value of social welfare attainable if all agents had pooled their information. In the important LQG case, the bid-price iteration is dramatically simple, exchanging only real-valued vectors of future prices and consumptions generations at each time step. Agents need not even know of the existence of other agents. DC power flow equations can also be incorporated. The results may be of broader interest vis-a-vis general equilibrium theory of economics for stochastic dynamic agents.