# Regression Equilibrium

arXiv: https://arxiv.org/abs/1905.02576 · HTML: https://mlsanity.com/paper/1905.02576/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2019.

## Built on by (most cited first, 16 of 16)

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- [Strategic Usage in a Multi-Learner Setting](https://mlsanity.com/paper/2401.16422/) (2024)
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- [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)
- [Long-term Data Sharing under Exclusivity Attacks](https://mlsanity.com/paper/2201.09137/) (2022)
- [Heterogeneous Data Game: Characterizing the Model Competition Across Multiple Data Sources](https://mlsanity.com/paper/2505.07688/) (2025)
- [Power and Limitations of Aggregation in Compound AI Systems](https://mlsanity.com/paper/2602.21556/) (2026)
- [Markets for Models](https://mlsanity.com/paper/2503.02946/) (2025)
- [Market Games for Generative Models: Equilibria, Welfare, and Strategic Entry](https://mlsanity.com/paper/2602.17787/) (2026)
- [Once-for-All: Scalable Simultaneous Forecasting via Equilibrium State Estimation](https://mlsanity.com/paper/2606.13285/) (2026)

## Abstract (arXiv)

Prediction is a well-studied machine learning task, and prediction algorithms are core ingredients in online products and services. Despite their centrality in the competition between online companies who offer prediction-based products, the textitstrategic use of prediction algorithms remains unexplored. The goal of this paper is to examine strategic use of prediction algorithms. We introduce a novel game-theoretic setting that is based on the PAC learning framework, where each player (aka a prediction algorithm aimed at competition) seeks to maximize the sum of points for which it produces an accurate prediction and the others do not. We show that algorithms aiming at generalization may wittingly mispredict some points to perform better than others on expectation. We analyze the empirical game, i.e., the game induced on a given sample, prove that it always possesses a pure Nash equilibrium, and show that every better-response learning process converges. Moreover, our learning-theoretic analysis suggests that players can, with high probability, learn an approximate pure Nash equilibrium for the whole population using a small number of samples.