# The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally

arXiv: https://arxiv.org/abs/1910.04123 · HTML: https://mlsanity.com/paper/1910.04123/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2019.

## Built on by (most cited first, 30 of 41)

- [Data Feedback Loops: Model-driven Amplification of Dataset Biases](https://mlsanity.com/paper/2209.03942/) (2022)
- [Information Discrepancy in Strategic Learning](https://mlsanity.com/paper/2103.01028/) (2021)
- [Modeling Content Creator Incentives on Algorithm-Curated Platforms](https://mlsanity.com/paper/2206.13102/) (2022)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [Fairness Transferability Subject to Bounded Distribution Shift](https://mlsanity.com/paper/2206.00129/) (2022)
- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [Strategic Ranking](https://mlsanity.com/paper/2109.08240/) (2021)
- [Unintended Selection: Persistent Qualification Rate Disparities and Interventions](https://mlsanity.com/paper/2111.01201/) (2021)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Algorithmic Fairness in Business Analytics: Directions for Research and Practice](https://mlsanity.com/paper/2207.10991/) (2022)
- [Runtime Monitoring of Dynamic Fairness Properties](https://mlsanity.com/paper/2305.04699/) (2023)
- [Learnability Gaps of Strategic Classification](https://mlsanity.com/paper/2402.19303/) (2024)
- [Improved Bayes Risk Can Yield Reduced Social Welfare Under Competition](https://mlsanity.com/paper/2306.14670/) (2023)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)
- [A Classification of Feedback Loops and Their Relation to Biases in Automated Decision-Making Systems](https://mlsanity.com/paper/2305.06055/) (2023)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [On the Actionability of Outcome Prediction](https://mlsanity.com/paper/2309.04470/) (2023)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [The Double-Edged Sword of Behavioral Responses in Strategic Classification: Theory and User Studies](https://mlsanity.com/paper/2410.18066/) (2024)
- [Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing](https://mlsanity.com/paper/2104.01634/) (2021)
- [Sequential Strategic Screening](https://mlsanity.com/paper/2301.13397/) (2023)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets](https://mlsanity.com/paper/2404.13240/) (2024)
- [Algorithmic Fairness in Performative Policy Learning: Escaping the Impossibility of Group Fairness](https://mlsanity.com/paper/2405.20447/) (2024)
- [Precarity: Modeling the Long Term Effects of Compounded Decisions on Individual Instability](https://mlsanity.com/paper/2104.12037/) (2021)
- [Adaptive Data Debiasing through Bounded Exploration](https://mlsanity.com/paper/2110.13054/) (2021)
- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Should Decision-Makers Reveal Classifiers in Online Strategic Classification?](https://mlsanity.com/paper/2506.01936/) (2025)
- [Scoring Rules for Performative Binary Prediction](https://mlsanity.com/paper/2207.02847/) (2022)

## Abstract (arXiv)

The long-term impact of algorithmic decision making is shaped by the dynamics between the deployed decision rule and individuals' response. Focusing on settings where each individual desires a positive classification---including many important applications such as hiring and school admissions, we study a dynamic learning setting where individuals invest in a positive outcome based on their group's expected gain and the decision rule is updated to maximize institutional benefit. By characterizing the equilibria of these dynamics, we show that natural challenges to desirable long-term outcomes arise due to heterogeneity across groups and the lack of realizability. We consider two interventions, decoupling the decision rule by group and subsidizing the cost of investment. We show that decoupling achieves optimal outcomes in the realizable case but has discrepant effects that may depend on the initial conditions otherwise. In contrast, subsidizing the cost of investment is shown to create better equilibria for the disadvantaged group even in the absence of realizability.