# Algorithmic Decision-Making under Agents with Persistent Improvement

arXiv: https://arxiv.org/abs/2405.01807 · HTML: https://mlsanity.com/paper/2405.01807/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 63 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 30 of 33)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [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)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (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)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Group Retention when Using Machine Learning in Sequential Decision Making: the Interplay between User Dynamics and Fairness](https://mlsanity.com/paper/1905.00569/) (2019)
- [Fairness in Learning-Based Sequential Decision Algorithms: A Survey](https://mlsanity.com/paper/2001.04861/) (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)
- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [Preference Dynamics Under Personalized Recommendations](https://mlsanity.com/paper/2205.13026/) (2022)
- [Strategic Classification under Unknown Personalized Manipulation](https://mlsanity.com/paper/2305.16501/) (2023)
- [Strategic Ranking](https://mlsanity.com/paper/2109.08240/) (2021)
- [From Predictions to Decisions: Using Lookahead Regularization](https://mlsanity.com/paper/2006.11638/) (2020)
- [Unintended Selection: Persistent Qualification Rate Disparities and Interventions](https://mlsanity.com/paper/2111.01201/) (2021)
- [Polarization in Geometric Opinion Dynamics](https://mlsanity.com/paper/2106.12459/) (2021)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)

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

- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [Addressing Polarization and Unfairness in Performative Prediction](https://mlsanity.com/paper/2406.16756/) (2024)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [How Strategic Agents Respond: Comparing Analytical Models with LLM-Generated Responses in Strategic Classification](https://mlsanity.com/paper/2501.16355/) (2025)
- [Anticipating Gaming to Incentivize Improvement: Guiding Agents in (Fair) Strategic Classification](https://mlsanity.com/paper/2505.05594/) (2025)
- [SPRINT: Stochastic Performative Prediction With Variance Reduction](https://mlsanity.com/paper/2509.17304/) (2025)
- [Linear Strategic Classification with Endogenous Improvements](https://mlsanity.com/paper/2606.01198/) (2026)

## Abstract (arXiv)

This paper studies algorithmic decision-making under human's strategic behavior, where a decision maker uses an algorithm to make decisions about human agents, and the latter with information about the algorithm may exert effort strategically and improve to receive favorable decisions. Unlike prior works that assume agents benefit from their efforts immediately, we consider realistic scenarios where the impacts of these efforts are persistent and agents benefit from efforts by making improvements gradually. We first develop a dynamic model to characterize persistent improvements and based on this construct a Stackelberg game to model the interplay between agents and the decision-maker. We analytically characterize the equilibrium strategies and identify conditions under which agents have incentives to improve. With the dynamics, we then study how the decision-maker can design an optimal policy to incentivize the largest improvements inside the agent population. We also extend the model to settings where 1) agents may be dishonest and game the algorithm into making favorable but erroneous decisions; 2) honest efforts are forgettable and not sufficient to guarantee persistent improvements. With the extended models, we further examine conditions under which agents prefer honest efforts over dishonest behavior and the impacts of forgettable efforts.