# Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty

arXiv: https://arxiv.org/abs/2502.06749 · HTML: https://mlsanity.com/paper/2502.06749/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 24 of 24)

- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Causal Machine Learning: A Survey and Open Problems](https://mlsanity.com/paper/2206.15475/) (2022)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [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)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [On classification of strategic agents who can both game and improve](https://mlsanity.com/paper/2203.00124/) (2022)
- [Improvement-Focused Causal Recourse (ICR)](https://mlsanity.com/paper/2210.15709/) (2022)
- [The Double-Edged Sword of Behavioral Responses in Strategic Classification: Theory and User Studies](https://mlsanity.com/paper/2410.18066/) (2024)
- [Price of Privacy in the Keynesian Beauty Contest](https://mlsanity.com/paper/1905.00844/) (2019)

## Built on by (most cited first, 8 of 8)

- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [The Disparate Effects of Partial Information in Bayesian Strategic Learning](https://mlsanity.com/paper/2506.00627/) (2025)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [The Role of Causality in Algorithmic Recourse](https://mlsanity.com/paper/2607.28497/) (2026)
- [Partial Fairness Awareness: Belief-Guided Strategic Mechanism for Strategic Agents](https://mlsanity.com/paper/2606.00826/) (2026)
- [Linear Strategic Classification with Endogenous Improvements](https://mlsanity.com/paper/2606.01198/) (2026)
- [Robust Strategic Classification under Decision-Dependent Cost Uncertainty](https://mlsanity.com/paper/2606.30136/) (2026)

## Abstract (arXiv)

We study strategic classification in binary decision-making settings where agents can modify their features in order to improve their classification outcomes. Importantly, our work considers the causal structure across different features, acknowledging that effort in a given feature may affect other features. The main goal of our work is to understand when and how much agent effort is invested towards desirable features, and how this is influenced by the deployed classifier, the causal structure of the agent's features, their ability to modify them, and the information available to the agent about the classifier and the feature causal graph. In the complete information case, when agents know the classifier and the causal structure of the problem, we derive conditions ensuring that rational agents focus on features favored by the principal. We show that designing classifiers to induce desirable behavior is generally non-convex, though tractable in special cases. We also extend our analysis to settings where agents have incomplete information about the classifier or the causal graph. While optimal effort selection is again a non-convex problem under general uncertainty, we highlight special cases of partial uncertainty where this selection problem becomes tractable. Our results indicate that uncertainty drives agents to favor features with higher expected importance and lower variance, potentially misaligning with principal preferences. Finally, numerical experiments based on a cardiovascular disease risk study illustrate how to incentivize desirable modifications under uncertainty.