Arbitrage-free Data Pricing

Abstract

We study optimal pricing of versioned data products when buyers can combine multiple purchases. A monopoly seller offers a menu of data products, and a buyer's value for data is the improvement to their expected utility in a Bayesian decision problem. Since a buyer may purchase any finite bundle of products, including repeated copies of the same product, versioning creates arbitrage opportunities: a bundle of cheaper products may be more valuable than a product with a higher price. We formulate the arbitrage-free data selling problem which has infinite arbitrage-free constraints in general and possibly infinite state space, and prove its computational intractability: the problem admits no PTAS even for instances in which the state space is finite, and the problem admits no polynomial time constant factor approximation for succinct high-dimensional instances. On the positive side, when the numbers of buyer types and actions are constant, we give an additive FPTAS that handles possibly infinite state spaces and infinitely many arbitrage-free constraints, and empirically validate the algorithm on realistic synthetic data trading scenarios. We also analyze the posted pricing algorithm for selling only complete information and prove a tight approximation factor. We further identify a threshold utility regime in which arbitrage-freeness reduces to Blackwell dominance, which unifies known arbitrage-free conditions for dataset query and machine learning model pricing. Under this regime, we design efficient algorithms for several structured data menus common in practice.