# Competition over data: how does data purchase affect users?

arXiv: https://arxiv.org/abs/2201.10774 · HTML: https://mlsanity.com/paper/2201.10774/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 26 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [Multiagent Cooperation and Competition with Deep Reinforcement Learning](https://mlsanity.com/paper/1511.08779/) (2015)
- [Stabilising Experience Replay for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1702.08887/) (2017)
- [Provable Self-Play Algorithms for Competitive Reinforcement Learning](https://mlsanity.com/paper/2002.04017/) (2020)
- [Learning Active Learning from Data](https://mlsanity.com/paper/1703.03365/) (2017)
- [Strategically Efficient Exploration in Competitive Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2107.14698/) (2021)

## Built on by (most cited first, 5 of 5)

- [Competition, Alignment, and Equilibria in Digital Marketplaces](https://mlsanity.com/paper/2208.14423/) (2022)
- [Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition](https://mlsanity.com/paper/2306.14670/) (2023)
- [Safety vs. Performance: How Multi-Objective Learning Reduces Barriers to Market Entry](https://mlsanity.com/paper/2409.03734/) (2024)
- [Strategic Usage in a Multi-Learner Setting](https://mlsanity.com/paper/2401.16422/) (2024)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)

## Abstract (arXiv)

As machine learning (ML) is deployed by many competing service providers, the underlying ML predictors also compete against each other, and it is increasingly important to understand the impacts and biases from such competition. In this paper, we study what happens when the competing predictors can acquire additional labeled data to improve their prediction quality. We introduce a new environment that allows ML predictors to use active learning algorithms to purchase labeled data within their budgets while competing against each other to attract users. Our environment models a critical aspect of data acquisition in competing systems which has not been well-studied before. We found that the overall performance of an ML predictor improves when predictors can purchase additional labeled data. Surprisingly, however, the quality that users experience -- i.e. the accuracy of the predictor selected by each user -- can decrease even as the individual predictors get better. We show that this phenomenon naturally arises due to a trade-off whereby competition pushes each predictor to specialize in a subset of the population while data purchase has the effect of making predictors more uniform. We support our findings with both experiments and theories.