# Who Leads and Who Follows in Strategic Classification?

arXiv: https://arxiv.org/abs/2106.12529 · HTML: https://mlsanity.com/paper/2106.12529/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 21 of 21)

- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [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)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [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)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [Kernel-based methods for bandit convex optimization](https://mlsanity.com/paper/1607.03084/) (2016)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [On Gradient-Based Learning in Continuous Games](https://mlsanity.com/paper/1804.05464/) (2018)
- [The Strategic Perceptron](https://mlsanity.com/paper/2008.01710/) (2020)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Bandit learning in concave N-person games](https://mlsanity.com/paper/1810.01925/) (2018)

## Built on by (most cited first, 30 of 53)

- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Algorithmic Collective Action in Machine Learning](https://mlsanity.com/paper/2302.04262/) (2023)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [ISAACS: Iterative Soft Adversarial Actor-Critic for Safety](https://mlsanity.com/paper/2212.03228/) (2022)
- [Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents](https://mlsanity.com/paper/2306.02704/) (2023)
- [Strategic Classification under Unknown Personalized Manipulation](https://mlsanity.com/paper/2305.16501/) (2023)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Fundamental Bounds on Online Strategic Classification](https://mlsanity.com/paper/2302.12355/) (2023)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments](https://mlsanity.com/paper/2208.11040/) (2022)
- [Diversified Recommendations for Agents with Adaptive Preferences](https://mlsanity.com/paper/2210.07773/) (2022)
- [Online Learning in a Creator Economy](https://mlsanity.com/paper/2305.11381/) (2023)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safety](https://mlsanity.com/paper/2409.13867/) (2024)
- [Incentivizing High-Quality Content in Online Recommender Systems](https://mlsanity.com/paper/2306.07479/) (2023)
- [Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets](https://mlsanity.com/paper/2404.13240/) (2024)
- [Statistical Collusion by Collectives on Learning Platforms](https://mlsanity.com/paper/2502.04879/) (2025)
- [PAC Learning with Improvements](https://mlsanity.com/paper/2503.03184/) (2025)
- [Strategic Distribution Shift of Interacting Agents via Coupled Gradient Flows](https://mlsanity.com/paper/2307.01166/) (2023)
- [Impact of Decentralized Learning on Player Utilities in Stackelberg Games](https://mlsanity.com/paper/2403.00188/) (2024)
- [Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions](https://mlsanity.com/paper/2408.08272/) (2024)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Should Decision-Makers Reveal Classifiers in Online Strategic Classification?](https://mlsanity.com/paper/2506.01936/) (2025)
- [Strategic Representation](https://mlsanity.com/paper/2206.08542/) (2022)
- [Strategic Classification with Non-Linear Classifiers](https://mlsanity.com/paper/2505.23443/) (2025)

## Abstract (arXiv)

As predictive models are deployed into the real world, they must increasingly contend with strategic behavior. A growing body of work on strategic classification treats this problem as a Stackelberg game: the decision-maker "leads" in the game by deploying a model, and the strategic agents "follow" by playing their best response to the deployed model. Importantly, in this framing, the burden of learning is placed solely on the decision-maker, while the agents' best responses are implicitly treated as instantaneous. In this work, we argue that the order of play in strategic classification is fundamentally determined by the relative frequencies at which the decision-maker and the agents adapt to each other's actions. In particular, by generalizing the standard model to allow both players to learn over time, we show that a decision-maker that makes updates faster than the agents can reverse the order of play, meaning that the agents lead and the decision-maker follows. We observe in standard learning settings that such a role reversal can be desirable for both the decision-maker and the strategic agents. Finally, we show that a decision-maker with the freedom to choose their update frequency can induce learning dynamics that converge to Stackelberg equilibria with either order of play.