Incentivizing Truthful Data Contributions in a Marketplace for Mean Estimation

2025-02-22

AI Summary

This paper studies how to incentivize heterogeneous-cost data contributors in a data market to truthfully report their data, enabling buyers to accurately estimate the mean of an unknown normal distribution while maximizing the broker’s profit. We propose the first mechanism that bridges data pricing with ordering-based item pricing (OIP), designing a dynamic pricing rule grounded in data consistency. This ensures participation and truthful reporting exclusively by the lowest-cost contributors, achieving a Nash equilibrium. The mechanism rigorously satisfies individual rationality, budget balance, and envy-freeness, and attains approximate incentive compatibility. We theoretically prove that its profit asymptotically approaches the optimal upper bound achievable by any mechanism under any Nash equilibrium. Furthermore, we disprove the existence of non-trivial deterministic strategyproof (DSIC) mechanisms for this setting.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Data transparency and provenance
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We study a data marketplace where a broker mediates transactions between buyers and contributors. Buyers estimate the mean mu of an unknown normal distribution N(mu, sigma^2), with valuations based on estimation error. Contributors, incurring different data collection costs, gather and report samples (not necessarily truthfully) to the broker, who sells subsets at varying prices and redistributes revenue. We model this as a mechanism design problem to maximize profit (revenue minus data costs) while ensuring individual rationality (participation benefits all), envy-freeness (no buyer prefers another allocation), budget balance (payments cover costs), and incentive compatibility (contributors truthfully report sufficient data). We design a mechanism which satisfies these requirements. We first establish a connection between envy-free data pricing and ordered-item pricing (OIP) for unit-demand buyers and leverage OIP algorithms to determine the optimal data allocation and expected prices for buyers. The actual prices paid by buyers are centered around these expected prices, but also vary based on discrepancies in contributors' reported data. This variation is then passed on to the contributors via their payments. This scheme results in a Nash equilibrium (NE) where only the two lowest-cost contributors collect all the data and report it truthfully. Including this variation in the prices also helps us achieve individual rationality for buyers, as buyers will pay less if there are significant discrepancies in contributors' datasets. To complement these findings, we prove a nearly matching upper bound on the maximum possible profit achievable in any NE of any mechanism, thus proving that our mechanism is essentially unimprovable. We also show that no nontrivial dominant-strategy incentive-compatible mechanism exists in this problem.

Problem

• Design a mechanism for truthful data contributions.
• Maximize profit while ensuring fairness and incentives.
• Establish optimal data allocation and pricing strategies.

Innovation

• Envy-free data pricing strategy
• Ordered-item pricing algorithm
• Nash equilibrium for truthfulness