Markets for Models
Krishna Dasaratha, Juan Ortner, Chengyang Zhu
TL;DR
The paper develops a microfounded theory of markets in which firms sell prediction models to a consumer who can form a weighted ensemble from multiple models. It shows that market outcomes can be characterized by the bias-variance decompositions of the models, linking statistical properties to entry, competition, and pricing, and demonstrates that symmetric firms may differentiate to extract higher surplus while incumbents can use biased or overly costly models to deter entry. The analysis covers simultaneous and sequential entry, proving that decreasing marginal returns yield efficient SPNEs but that differentiation and deterrence can generate inefficiencies and even monopoly outcomes. Overall, improving model quality (lower variance) tends to reduce total surplus through reduced entry but increases consumer welfare when competition is limited, highlighting a nuanced trade-off between competition and predictive accuracy. The framework provides a lens for understanding real-world AI and data markets, including the emergence of data moats and differentiated data sources, underlining the impact of bias-variance tradeoffs on market structure and welfare.
Abstract
Motivated by the prevalence of prediction problems in the economy, we study markets in which firms sell models to a consumer to help improve their prediction. Firms decide whether to enter, choose models to train on their data, and set prices. The consumer can purchase multiple models and use a weighted average of the models bought. Market outcomes can be expressed in terms of the \emph{bias-variance decompositions} of the models that firms sell. We give conditions when symmetric firms will choose different modeling techniques, e.g., each using only a subset of available covariates. We also show firms can choose inefficiently biased models or inefficiently costly models to deter entry by competitors.