# Markets for Models

arXiv: https://arxiv.org/abs/2503.02946 · HTML: https://mlsanity.com/paper/2503.02946/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 10 of 10)

- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Algorithmic Monoculture and Social Welfare](https://mlsanity.com/paper/2101.05853/) (2021)
- [Regression Equilibrium](https://mlsanity.com/paper/1905.02576/) (2019)
- [Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition](https://mlsanity.com/paper/2306.14670/) (2023)
- [Competing Bandits: The Perils of Exploration Under Competition](https://mlsanity.com/paper/2007.10144/) (2020)
- [Bias-Variance Games](https://mlsanity.com/paper/1909.03618/) (2019)
- [Pricing and Competition for Generative AI](https://mlsanity.com/paper/2411.02661/) (2024)
- [Safety vs. Performance: How Multi-Objective Learning Reduces Barriers to Market Entry](https://mlsanity.com/paper/2409.03734/) (2024)
- [Competing Models](https://mlsanity.com/paper/1907.03809/) (2019)

## Abstract (arXiv)

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 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.