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 preliminary announcement of some of these results was presented in the conference paper @cite_19 . The layered payment structure for LQG systems is mentioned there, and incentive compatibility results are presented without proofs. The present paper contains the complete proof of incentive compatibility, and further introduces the Scaled VCG mechanism for budget balance, individual rationality, and Lagrange optimality.
@cite_19
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The classic Vickrey-Clarke-Groves (VCG) mechanism ensures incentive compatibility, 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 over time, the agents' intertemporal payoffs depend on the expected future controls and payments, and a direct extension of the VCG mechanism is not sufficient to guarantee incentive compatibility. In fact, it does not appear to be feasible to construct mechanisms that ensure the dominance of dynamic truth-telling for agents comprised of general stochastic dynamic systems. The contribution of this paper is to show that such a dynamic stochastic extension does exist for the special case of Linear-Quadratic-Gaussian (LQG) agents with a careful construction of a sequence of layered payments over time. We propose a layered version of a modified VCG mechanism for payments that decouples the intertemporal effect of current bids on future payoffs, and prove that truth-telling of dynamic states forms a dominant strategy if system parameters are known and agents are rational. An important example of a problem needing such optimal dynamic coordination of stochastic agents arises in power systems where an Independent System Operator (ISO) has to ensure balance of generation and consumption at all time instants, while ensuring social optimality (maximization of the sum of the utilities of all agents). Addressing strategic behavior is critical as the price-taking assumption on market participants may not hold in an electricity market. Agents, can lie or otherwise game the bidding system. The challenge is to determine a bidding scheme between all agents and the ISO that maximizes social welfare, while taking into account the stochastic dynamic models of agents, since renewable energy resources such as solar wind are stochastic and dynamic in nature, as are consumptions by loads which are influenced by factors such as local temperatures and thermal inertias of facilities.