Data-Driven Mechanism Design: Jointly Eliciting Preferences and Information

2024-12-20

ACM Conference on Economics and Computation

AI Summary

This paper addresses the inefficiency of standard mechanisms (e.g., VCG) in multidimensional type environments where agents hold both private preferences and shared, uncertain state information affecting common values. To restore social efficiency, we propose a novel mechanism design framework that integrates posterior behavioral data (e.g., user feedback) into incentive-compatible allocation. Our key innovation is the first incorporation of a state estimator directly within a VCG-style mechanism, yielding a theory of implementation grounded in posterior equilibrium. The framework unifies three canonical settings: full revelation, affine utilities, and consistent estimation—achieving exact social optimality in the first two, and asymptotic optimality in the third, with estimation error decaying at an explicit rate as estimator accuracy improves. Methodologically, we bridge Bayesian mechanism design, state estimation theory, and VCG extensions. We validate the framework through formal models of digital advertising auctions and LLM-based human–AI interaction.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We study mechanism design when agents have private preferences and private information about 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 payoff-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 affine 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. A full version of this paper can be found at https://arxiv.org/abs/2412.16132.

Problem

• Design mechanisms for agents with private preferences and information.
• Extend VCG framework using data-driven transfers for efficient allocations.
• Apply to auctions and AI assistants where information is revealed post-allocation.

Innovation

• Data-driven mechanisms condition transfers on post-allocation information
• Extend Vickrey-Clarke-Groves framework for multi-dimensional private types
• Achieve exact or approximate implementation using state estimators