# Incentive Compatibility in Stochastic Dynamic Systems

## TL;DR

This paper develops mechanisms for stochastic dynamic systems with LQG agents that ensure incentive compatibility and social efficiency, extending classic static mechanisms to dynamic, uncertain environments.

## Contribution

It introduces a layered payment mechanism for LQG agents that decouples intertemporal effects and a scaled VCG mechanism satisfying multiple economic properties.

## Key findings

- Layered payments ensure truth-telling in dynamic stochastic systems.
- Scaled VCG mechanism achieves incentive compatibility, efficiency, and budget balance.
- Payments converge to true prices as the number of agents increases.

## Abstract

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.