Markets for Models

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 bias-variance decompositions of the models that firms sell. We show that market structure can depend in subtle and nonmonotonic ways on the statistical properties of available models. Moreover, firms may choose inefficiently biased models to deter entry by competitors or to obtain larger profits.