# Algorithmic Recourse Under Competition

arXiv: https://arxiv.org/abs/2609.39877 · HTML: https://mlsanity.com/paper/2609.39877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 52 of its 65 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 30 of 52)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Equalizing Recourse across Groups](https://mlsanity.com/paper/1909.03166/) (2019)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Difficult Lessons on Social Prediction from Wisconsin Public Schools](https://mlsanity.com/paper/2304.06205/) (2023)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Amortized Generation of Sequential Algorithmic Recourses for Black-box Models](https://mlsanity.com/paper/2106.03962/) (2021)
- [Improvement-Focused Causal Recourse (ICR)](https://mlsanity.com/paper/2210.15709/) (2022)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)
- [Promoting Counterfactual Robustness through Diversity](https://mlsanity.com/paper/2312.06564/) (2023)
- [Equal Improvability: A New Fairness Notion Considering the Long-term Impact](https://mlsanity.com/paper/2210.06732/) (2022)

## Abstract (arXiv)

Algorithmic recourse provides individuals who have received undesirable outcomes from machine learning models with suggestions for minimum-cost improvements to achieve the desired outcome. A central assumption when computing recourse is that the decision rule remains fixed throughout the recourse implementation phase. We challenge this assumption in settings where individuals compete for limited resources. In such settings, widespread recourse implementation can change the acceptance threshold even when the scoring model that is used to evaluate individuals remains the same. This change in acceptance threshold can, in turn, invalidate the original recourse recommendations (i.e., following the recourse may not lead to the desired outcome). To address this problem, we introduce a framework called recourse under competition that jointly optimizes for recommendation recipients and the recommended score target they need to satisfy to balance the recourse cost and post-shift validity among initially rejected individuals. We develop an algorithm based on the Implicit Function Theorem and empirically analyze its performance. Experiments on synthetic and real datasets show that personalized score targets can achieve higher validity, albeit at a higher cost. In contrast, common score targets generally offer favorable cost-validity trade-offs for lower to medium validity values.