# Strategic Classification With Externalities

arXiv: https://arxiv.org/abs/2410.08032 · HTML: https://mlsanity.com/paper/2410.08032/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 46 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 25 of 25)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Strategyproof Linear Regression in High Dimensions](https://mlsanity.com/paper/1805.10693/) (2018)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [Towards Data Auctions with Externalities](https://mlsanity.com/paper/2003.08345/) (2020)
- [Equalizing Credit Opportunity in Algorithms: Aligning Algorithmic Fairness Research with U.S. Fair Lending Regulation](https://mlsanity.com/paper/2210.02516/) (2022)
- [Equilibrium of Data Markets with Externality](https://mlsanity.com/paper/2302.08012/) (2023)
- [The Effect of Strategic Noise in Linear Regression](https://mlsanity.com/paper/2007.07316/) (2020)

## Built on by (most cited first, 7 of 7)

- [A Market for Accuracy: Classification under Competition](https://mlsanity.com/paper/2502.18052/) (2025)
- [Strategic Classification with Non-Linear Classifiers](https://mlsanity.com/paper/2505.23443/) (2025)
- [Learning Classifiers That Induce Markets](https://mlsanity.com/paper/2502.20012/) (2025)
- [Welfare as a Guiding Principle for Machine Learning -- From Compass, to Lens, to Roadmap](https://mlsanity.com/paper/2502.11981/) (2025)
- [Learning to Play Multi-Follower Bayesian Stackelberg Games](https://mlsanity.com/paper/2510.01387/) (2025)
- [Power and Limitations of Aggregation in Compound AI Systems](https://mlsanity.com/paper/2602.21556/) (2026)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)

## Abstract (arXiv)

We propose a new variant of the strategic classification problem: a principal reveals a classifier, and n agents report their (possibly manipulated) features to be classified. Motivated by real-world applications, our model crucially allows the manipulation of one agent to affect another; that is, it explicitly captures inter-agent externalities. The principal-agent interactions are formally modeled as a Stackelberg game, with the resulting agent manipulation dynamics captured as a simultaneous game. We show that under certain assumptions, the pure Nash Equilibrium of this agent manipulation game is unique and can be efficiently computed. Leveraging this result, PAC learning guarantees are established for the learner: informally, we show that it is possible to learn classifiers that minimize loss on the distribution, even when a random number of agents are manipulating their way to a pure Nash Equilibrium. We also comment on the optimization of such classifiers through gradient-based approaches. This work sets the theoretical foundations for a more realistic analysis of classifiers that are robust against multiple strategic actors interacting in a common environment.