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The classic Vickrey-Clarke-Groves (VCG) mechanism ensures incentivecompatibility, i.e., that truth-telling of all agents is a dominant strategy,for a static one-shot game. However, in a dynamic environment that unfolds overtime, the agents' intertemporal payoffs depend on the expected future controlsand payments, and a direct extension of the VCG mechanism is not sufficient toguarantee incentive compatibility. In fact, it does not appear to be feasibleto construct mechanisms that ensure the dominance of dynamic truth-telling foragents comprised of general stochastic dynamic systems. The contribution ofthis paper is to show that such a dynamic stochastic extension does exist forthe special case of Linear-Quadratic-Gaussian (LQG) agents with a carefulconstruction of a sequence of layered payments over time. For a set of LQGagents, we propose a modified layered version of the VCG mechanism for paymentsthat decouples the intertemporal effect of current bids on future payoffs, andprove that truth-telling of dynamic states forms a dominant strategy if systemparameters are known and agents are rational.  An important example of a problem needing such optimal dynamic coordinationof stochastic agents arises in power systems where an Independent SystemOperator (ISO) has to ensure balance of generation and consumption at all timeinstants, while ensuring social optimality. The challenge is to determine abidding scheme between all agents and the ISO that maximizes social welfare,while taking into account the stochastic dynamic models of agents, sincerenewable energy resources such as solar/wind are stochastic and dynamic innature, as are consumptions by loads which are influenced by factors such aslocal temperatures and thermal inertias of facilities.

The Strategic LQG System: A Dynamic Stochastic VCG Framework for Optimal Coordination