How to Price Data: A Market Equilibrium Based Approach

High-quality data is a key input to modern machine learning models, leading to the emergence of platforms that facilitate the buying and selling of data. A central challenge in these platforms is how the data is priced to balance the interests of both buyers and sellers. Traditional market equilibrium notions, where demand meets supply are commonly used to price goods but do not extend naturally to data due to its non-rivalrous nature, whereby multiple buyers can simultaneously benefit from the same dataset. We therefore introduce a new notion of equilibrium for data pricing based on Nash equilibrium and study it in settings where data may be complementary or substitutable, focusing on the canonical utility models for each, namely Leontief and linear, respectively. We show that equilibrium prices fail to exist for linear utilities even with homogeneous buyers and two sellers, while establishing strong existence, efficiency, and polynomial-time computation guarantees for Leontief utilities in general markets with $n$ homogeneous buyers and $m$ sellers. We further examine the role of platform mediation and price discrimination in enabling *optimal* equilibrium outcomes efficiently. On the technical front, we develop a novel proof technique based on systematically reducing the space of candidate equilibria through the *graph-of-deviations*, which may be of independent interest.

We look at the problem of pricing datasets in a market with sellers who have datasets to sell and buyers who are constrained by some budget on how much they can buy. We look at the problem when the buyers can have different valuations over the datasets of the sellers. If the buyer valuations are complementary -- i.e., when they obtain datasets from multiple sellers, their value is higher than if they obtain datasets from individual sellers, under certain assumptions, we show that equilibrium exists and can be computed efficiently. When the buyer valuations are substitutes i.e., having more datasets gives an increase in value but is less than the sum of values of the individual datasets, then under certain assumptions on the valuations, equilibrium only exists under price-discrimination. This is one of the first papers to study data market design with equilibrium pricing in presence of competition. We believe that lot of follow up work is possible and our paper has ideas that can contribute to this follow up work.