# Competition, Alignment, and Equilibria in Digital Marketplaces

arXiv: https://arxiv.org/abs/2208.14423 · HTML: https://mlsanity.com/paper/2208.14423/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 41 references that are in the map.
- First posted on arXiv 30 Aug 2022.

## Builds on (most cited first, 8 of 8)

- [Bayesian Incentive-Compatible Bandit Exploration](https://mlsanity.com/paper/1502.04147/) (2015)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Bayesian Exploration: Incentivizing Exploration in Bayesian Games](https://mlsanity.com/paper/1602.07570/) (2016)
- [The Price of Incentivizing Exploration: A Characterization via Thompson Sampling and Sample Complexity](https://mlsanity.com/paper/2002.00558/) (2020)
- [Regression Equilibrium](https://mlsanity.com/paper/1905.02576/) (2019)
- [Multiplayer Bandit Learning, from Competition to Cooperation](https://mlsanity.com/paper/1908.01135/) (2019)
- [Competing Bandits: The Perils of Exploration Under Competition](https://mlsanity.com/paper/2007.10144/) (2020)
- [Competition over data: how does data purchase affect users?](https://mlsanity.com/paper/2201.10774/) (2022)

## Built on by (most cited first, 17 of 17)

- [Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition](https://mlsanity.com/paper/2306.14670/) (2023)
- [Learning with Exposure Constraints in Recommendation Systems](https://mlsanity.com/paper/2302.01377/) (2023)
- [Algorithmic Collective Action in Recommender Systems: Promoting Songs by Reordering Playlists](https://mlsanity.com/paper/2404.04269/) (2024)
- [Two-sided Competing Matching Recommendation Markets With Quota and Complementary Preferences Constraints](https://mlsanity.com/paper/2301.10230/) (2023)
- [Choosing the Better Bandit Algorithm under Data Sharing: When Do A/B Experiments Work?](https://mlsanity.com/paper/2507.11891/) (2025)
- [Decongestion by Representation: Learning to Improve Economic Welfare in Marketplaces](https://mlsanity.com/paper/2306.10606/) (2023)
- [Train 'n Trade: Foundations of Parameter Markets](https://mlsanity.com/paper/2312.04740/) (2023)
- [Strategic Usage in a Multi-Learner Setting](https://mlsanity.com/paper/2401.16422/) (2024)
- [Evaluating Sample Utility for Efficient Data Selection by Mimicking Model Weights](https://mlsanity.com/paper/2501.06708/) (2025)
- [Learning Classifiers That Induce Markets](https://mlsanity.com/paper/2502.20012/) (2025)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)
- [Welfare as a Guiding Principle for Machine Learning -- From Compass, to Lens, to Roadmap](https://mlsanity.com/paper/2502.11981/) (2025)
- [Heterogeneous Data Game: Characterizing the Model Competition Across Multiple Data Sources](https://mlsanity.com/paper/2505.07688/) (2025)
- [Decoupled SGDA for Games with Intermittent Strategy Communication](https://mlsanity.com/paper/2501.14652/) (2025)
- [Data Sharing with a Generative AI Competitor](https://mlsanity.com/paper/2505.12386/) (2025)
- [Market Design for AI: Beyond the Copyright Binary](https://mlsanity.com/paper/2606.12260/) (2026)
- [The User Asks, Platforms Compete: How Agentic Recommendation Markets Take Shape](https://mlsanity.com/paper/2607.25253/) (2026)

## Abstract (arXiv)

Competition between traditional platforms is known to improve user utility by aligning the platform's actions with user preferences. But to what extent is alignment exhibited in data-driven marketplaces? To study this question from a theoretical perspective, we introduce a duopoly market where platform actions are bandit algorithms and the two platforms compete for user participation. A salient feature of this market is that the quality of recommendations depends on both the bandit algorithm and the amount of data provided by interactions from users. This interdependency between the algorithm performance and the actions of users complicates the structure of market equilibria and their quality in terms of user utility. Our main finding is that competition in this market does not perfectly align market outcomes with user utility. Interestingly, market outcomes exhibit misalignment not only when the platforms have separate data repositories, but also when the platforms have a shared data repository. Nonetheless, the data sharing assumptions impact what mechanism drives misalignment and also affect the specific form of misalignment (e.g. the quality of the best-case and worst-case market outcomes). More broadly, our work illustrates that competition in digital marketplaces has subtle consequences for user utility that merit further investigation.