Privacy Data Pricing: A Stackelberg Game Approach

TL;DR

This paper introduces a Stackelberg game model for pricing differentially private data, balancing privacy constraints and market value, and derives equilibrium strategies for data sellers and buyers.

Contribution

It develops a novel game-theoretic framework for privacy-aware data pricing incorporating differential privacy and derives closed-form equilibrium solutions.

Findings

Closed-form solutions for optimal pricing and privacy levels.

Boundary conditions for market participation under DP constraints.

Extension to nonlinear pricing functions.

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.