# Strategic Usage in a Multi-Learner Setting

arXiv: https://arxiv.org/abs/2401.16422 · HTML: https://mlsanity.com/paper/2401.16422/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 43 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 22 of 22)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (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)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [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)
- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Group Retention when Using Machine Learning in Sequential Decision Making: the Interplay between User Dynamics and Fairness](https://mlsanity.com/paper/1905.00569/) (2019)
- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Competition, Alignment, and Equilibria in Digital Marketplaces](https://mlsanity.com/paper/2208.14423/) (2022)
- [Regression Equilibrium](https://mlsanity.com/paper/1905.02576/) (2019)
- [Competing Bandits: The Perils of Exploration Under Competition](https://mlsanity.com/paper/2007.10144/) (2020)
- [Strategic Apple Tasting](https://mlsanity.com/paper/2306.06250/) (2023)
- [Coopetition Against an Amazon](https://mlsanity.com/paper/2005.10038/) (2020)
- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)
- [Competition over data: how does data purchase affect users?](https://mlsanity.com/paper/2201.10774/) (2022)
- [Algorithmic Censoring in Dynamic Learning Systems](https://mlsanity.com/paper/2305.09035/) (2023)

## Built on by (most cited first, 3 of 3)

- [Safety vs. Performance: How Multi-Objective Learning Reduces Barriers to Market Entry](https://mlsanity.com/paper/2409.03734/) (2024)
- [Learning Classifiers That Induce Markets](https://mlsanity.com/paper/2502.20012/) (2025)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)

## Abstract (arXiv)

Real-world systems often involve some pool of users choosing between a set of services. With the increase in popularity of online learning algorithms, these services can now self-optimize, leveraging data collected on users to maximize some reward such as service quality. On the flipside, users may strategically choose which services to use in order to pursue their own reward functions, in the process wielding power over which services can see and use their data. Extensive prior research has been conducted on the effects of strategic users in single-service settings, with strategic behavior manifesting in the manipulation of observable features to achieve a desired classification; however, this can often be costly or unattainable for users and fails to capture the full behavior of multi-service dynamic systems. As such, we analyze a setting in which strategic users choose among several available services in order to pursue positive classifications, while services seek to minimize loss functions on their observations. We focus our analysis on realizable settings, and show that naive retraining can still lead to oscillation even if all users are observed at different times; however, if this retraining uses memory of past observations, convergent behavior can be guaranteed for certain loss function classes. We provide results obtained from synthetic and real-world data to empirically validate our theoretical findings.