# How Strategic Agents Respond: Comparing Analytical Models with LLM-Generated Responses in Strategic Classification

arXiv: https://arxiv.org/abs/2501.16355 · HTML: https://mlsanity.com/paper/2501.16355/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 33 of its 61 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Out of One, Many: Using Language Models to Simulate Human Samples](https://mlsanity.com/paper/2209.06899/) (2022)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [The political ideology of conversational AI: Converging evidence on ChatGPT's pro-environmental, left-libertarian orientation](https://mlsanity.com/paper/2301.01768/) (2023)
- [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)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Can Large Language Model Agents Simulate Human Trust Behavior?](https://mlsanity.com/paper/2402.04559/) (2024)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)
- [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)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (2020)
- [Do LLM Agents Have Regret? A Case Study in Online Learning and Games](https://mlsanity.com/paper/2403.16843/) (2024)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Strategic Classification under Unknown Personalized Manipulation](https://mlsanity.com/paper/2305.16501/) (2023)
- [PATIENT-Psi: Using Large Language Models to Simulate Patients for Training Mental Health Professionals](https://mlsanity.com/paper/2405.19660/) (2024)
- [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)
- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [The Double-Edged Sword of Behavioral Responses in Strategic Classification: Theory and User Studies](https://mlsanity.com/paper/2410.18066/) (2024)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)

## Built on by (most cited first, 5 of 5)

- [BiasCause: Evaluate Socially Biased Causal Reasoning of Large Language Models](https://mlsanity.com/paper/2504.07997/) (2025)
- [Revealing Positive and Negative Role Models to Help People Make Good Decisions](https://mlsanity.com/paper/2603.02495/) (2026)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [RLRF: Competitive Search Agent Design via Reinforcement Learning from Ranker Feedback](https://mlsanity.com/paper/2510.04096/) (2025)
- [Shaping Human-AI Interactions to Provide Improvement Pathways and Balance Competing Objectives](https://mlsanity.com/paper/2608.05710/) (2026)

## Abstract (arXiv)

When ML algorithms are deployed to automate human-related decisions, human agents may learn the underlying decision policies and adapt their behavior. Strategic Classification (SC) has emerged as a framework for studying this interaction between agents and decision-makers to design more trustworthy ML systems. Prior theoretical models in SC assume that agents are perfectly or approximately rational and respond to decision policies by optimizing their utility. However, the growing prevalence of LLMs raises the possibility that real-world agents may instead rely on these tools for strategic advice. This shift prompts two questions: (i) Can LLMs generate effective and socially responsible strategies in SC settings? (ii) Can existing SC theoretical models accurately capture agent behavior when agents follow LLM-generated advice? To investigate these questions, we examine five critical SC scenarios: hiring, loan applications, school admissions, personal income, and public assistance programs. We simulate agents with diverse profiles who interact with three commercial LLMs (GPT-4o, GPT-4.1, and GPT-5), following their suggestions on effort allocations on features. We compare the resulting agent behaviors with the best responses in existing SC models. Our findings show that: (i) Even without access to the decision policy, LLMs can generate effective strategies that improve both agents' scores and qualification; (ii) At the population level, LLM-guided effort allocation strategies yield similar or even higher score improvements, qualification rates, and fairness metrics as those predicted by the SC theoretical model, suggesting that the theoretical model may still serve as a reasonable proxy for LLM-influenced behavior; and (iii) At the individual level, LLMs tend to produce more diverse and balanced effort allocations than theoretical models.