We study mechanism design when agents hold private information about both their preferences and a common payoff-relevant state. We show that standard message-driven mechanisms cannot implement socially efficient allocations when agents have multidimensional types, even under favorable conditions.
To overcome this limitation, we propose data-driven mechanisms that leverage additional post-allocation information, modeled as an estimator of the pay-off relevant state. Our data-driven mechanisms extend the classic Vickrey-Clarke-Groves class. We show that they achieve exact implementation in posterior equilibrium when the state is either fully revealed or the utility is linear in an unbiased estimator. We also show that they achieve approximate implementation with a consistent estimator, converging to exact implementation as the estimator converges, and present bounds on the convergence rate. We demonstrate applications to digital advertising auctions and large language model (llm) - based mechanisms, where user engagement naturally reveals relevant information.