# Using Cognitive Models to Improve Language Model Simulation of Human Persuasion Games

arXiv: https://arxiv.org/abs/2606.17657 · HTML: https://mlsanity.com/paper/2606.17657/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 72 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 30 of 35)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [LLM Agents Grounded in Self-Reports Enable General-Purpose Simulation of Individuals](https://mlsanity.com/paper/2411.10109/) (2024)
- [Personalizing Reinforcement Learning from Human Feedback with Variational Preference Learning](https://mlsanity.com/paper/2408.10075/) (2024)
- [Personalized Language Modeling from Personalized Human Feedback](https://mlsanity.com/paper/2402.05133/) (2024)
- [Generative agent-based modeling with actions grounded in physical, social, or digital space using Concordia](https://mlsanity.com/paper/2312.03664/) (2023)
- [On the Conversational Persuasiveness of Large Language Models: A Randomized Controlled Trial](https://mlsanity.com/paper/2403.14380/) (2024)
- [How Well Can LLMs Negotiate? NegotiationArena Platform and Analysis](https://mlsanity.com/paper/2402.05863/) (2024)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [Turning large language models into cognitive models](https://mlsanity.com/paper/2306.03917/) (2023)
- [Is In-Context Learning in Large Language Models Bayesian? A Martingale Perspective](https://mlsanity.com/paper/2406.00793/) (2024)
- [Large Language Models Assume People are More Rational than We Really are](https://mlsanity.com/paper/2406.17055/) (2024)
- [Chasing Moving Targets with Online Self-Play Reinforcement Learning for Safer Language Models](https://mlsanity.com/paper/2506.07468/) (2025)
- [Consistently Simulating Human Personas with Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2511.00222/) (2025)
- [A Mechanism-Based Approach to Mitigating Harms from Persuasive Generative AI](https://mlsanity.com/paper/2404.15058/) (2024)
- [Incoherent Probability Judgments in Large Language Models](https://mlsanity.com/paper/2401.16646/) (2024)
- [NitroGen: An Open Foundation Model for Generalist Gaming Agents](https://mlsanity.com/paper/2601.02427/) (2026)
- [Measuring General Intelligence with Generated Games](https://mlsanity.com/paper/2505.07215/) (2025)
- [Open Character Training: Shaping the Persona of AI Assistants through Constitutional AI](https://mlsanity.com/paper/2511.01689/) (2025)
- [The Levers of Political Persuasion with Conversational AI](https://mlsanity.com/paper/2507.13919/) (2025)
- [Toward Efficient Exploration by Large Language Model Agents](https://mlsanity.com/paper/2504.20997/) (2025)
- [Efficacy of Language Model Self-Play in Non-Zero-Sum Games](https://mlsanity.com/paper/2406.18872/) (2024)
- [Evaluating Generalization Capabilities of LLM-Based Agents in Mixed-Motive Scenarios Using Concordia](https://mlsanity.com/paper/2512.03318/) (2025)
- [AI Gamestore: Scalable, Open-Ended Evaluation of Machine General Intelligence with Human Games](https://mlsanity.com/paper/2602.17594/) (2026)
- [Levels of Analysis for Large Language Models](https://mlsanity.com/paper/2503.13401/) (2025)
- [Towards Strategic Persuasion with Language Models](https://mlsanity.com/paper/2509.22989/) (2025)
- [Are Large Language Models Sensitive to the Motives Behind Communication?](https://mlsanity.com/paper/2510.19687/) (2025)
- [Commercial Persuasion in AI-Mediated Conversations](https://mlsanity.com/paper/2604.04263/) (2026)

## Built on by (most cited first, 2 of 2)

- [RealCompanion: Benchmarking Human Understanding from Reasoning over Longitudinal Real-World Conversations](https://mlsanity.com/paper/2610.01780/) (2026)
- [Understanding and Reducing Misalignment in Persuasion Optimization](https://mlsanity.com/paper/2610.16070/) (2026)

## Abstract (arXiv)

People make decisions differently in strategic interactions. Some update beliefs like a Bayesian; others exhibit biases like motivated reasoning. Although creators of large language models use simulated humans for safety evaluations and training, they often fail to cover this breadth of human behavior. We argue that cognitive science and economics provide a convenient tool for doing so, making use of mathematical models of human decision-making. We propose an approach that we call Equation-to-Behavior Prompting for guiding large language models to match cognitive models, and evaluate this approach on persuasion games based on legal decision-making. We find that large models can approximate equation-based specifications -- Bayesian updating, affine distortion, motivated updating, and Grether's α-β model -- using prompting, but small models fail to do so. However, training small models with reinforcement learning to adhere to mathematical rules, Equation-to-Behavior RL, reduces belief error by 26.5% in out-of-distribution parameterizations. We show that these simulations can help create diverse training environments; training small models to consider different kinds of decision-makers improves average belief change by 2.5%--12% over Bayesian-only training, even when persuading GPT-5-mini. Our work could improve human simulations for training and evaluation in increasingly realistic settings, and could also enable novel research into more complicated mathematical models of human decision-making.