Privacy Data Pricing: A Stackelberg Game Approach

2025-12-20

AI Summary

This paper addresses the fundamental privacy–utility trade-off in differentially private (DP) data markets. We propose the first pricing framework that embeds the DP privacy–utility relationship into a Stackelberg leader–follower game: the market operator (leader) designs a price function, while buyers (followers) select optimal query accuracy under their privacy budget constraints. Our method analytically derives closed-form equilibrium solutions for both linear and power-function pricing schemes, explicitly characterizing the optimal noise variance, equilibrium price, and buyer participation threshold. By integrating differential privacy theory, game theory, and mechanism design, we establish a computationally tractable pricing foundation that simultaneously ensures incentive compatibility and rigorous DP guarantees.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Privacy
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Data markets are emerging as key mechanisms for trading personal and organizational data. Traditional data pricing studies -- such as query-based or arbitrage-free pricing models -- mainly emphasize price consistency and profit maximization but often neglect privacy constraints and strategic interactions. The widespread adoption of differential privacy (DP) introduces a fundamental privacy-utility trade-off: noise protects individuals' privacy but reduces data accuracy and market value. This paper develops a Stackelberg game framework for pricing DP data, where the market maker (leader) sets the price function and the data buyer (follower) selects the optimal query precision under DP constraints. We derive the equilibrium strategies for both parties under a balanced pricing function where the pricing decision variable enters linearly into the original pricing model. We obtain closed-form solutions for the optimal variance and pricing level, and determine the boundary conditions for market participation. Furthermore, we extend the analysis to Stackelberg games involving nonlinear power pricing functions. The model bridges DP and economic mechanism design, offering a unified foundation for incentive-compatible and privacy-conscious data pricing in data markets.

Problem

• Develops a Stackelberg game for pricing differentially private data
• Derives equilibrium strategies and closed-form solutions for optimal pricing
• Bridges differential privacy with economic mechanism design for data markets

Innovation

• Stackelberg game framework for differential privacy data pricing
• Closed-form solutions for optimal variance and pricing levels
• Extension to nonlinear power pricing functions in data markets