# LLM Strategic Reasoning: Agentic Study through Behavioral Game Theory

arXiv: https://arxiv.org/abs/2502.20432 · HTML: https://mlsanity.com/paper/2502.20432/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 23 of its 65 references that are in the map.
- First posted on arXiv 27 Feb 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 23 of 23)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [Bias Runs Deep: Implicit Reasoning Biases in Persona-Assigned LLMs](https://mlsanity.com/paper/2311.04892/) (2023)
- [Are We Done with MMLU?](https://mlsanity.com/paper/2406.04127/) (2024)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Granite Code Models: A Family of Open Foundation Models for Code Intelligence](https://mlsanity.com/paper/2405.04324/) (2024)
- [LLM as a Mastermind: A Survey of Strategic Reasoning with Large Language Models](https://mlsanity.com/paper/2404.01230/) (2024)
- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [How Far Are We on the Decision-Making of LLMs? Evaluating LLMs' Gaming Ability in Multi-Agent Environments](https://mlsanity.com/paper/2403.11807/) (2024)
- [Game-theoretic LLM: Agent Workflow for Negotiation Games](https://mlsanity.com/paper/2411.05990/) (2024)
- [Exploring Prosocial Irrationality for LLM Agents: A Social Cognition View](https://mlsanity.com/paper/2405.14744/) (2024)
- [Application of LLM Agents in Recruitment: A Novel Framework for Resume Screening](https://mlsanity.com/paper/2401.08315/) (2024)
- [K-Level Reasoning: Establishing Higher Order Beliefs in Large Language Models for Strategic Reasoning](https://mlsanity.com/paper/2402.01521/) (2024)
- [Contextual Moral Value Alignment Through Context-Based Aggregation](https://mlsanity.com/paper/2403.12805/) (2024)
- [Rational Tuning of LLM Cascades via Probabilistic Modeling](https://mlsanity.com/paper/2501.09345/) (2025)
- [Large Language Models Playing Mixed Strategy Nash Equilibrium Games](https://mlsanity.com/paper/2406.10574/) (2024)
- [An Experimental Study of Competitive Market Behavior Through LLMs](https://mlsanity.com/paper/2409.08357/) (2024)

## Built on by (most cited first, 17 of 17)

- [Base Models Beat Aligned Models at Randomness and Creativity](https://mlsanity.com/paper/2505.00047/) (2025)
- [AgenticPay: A Multi-Agent LLM Negotiation System for Buyer-Seller Transactions](https://mlsanity.com/paper/2602.06008/) (2026)
- [Beyond Nash Equilibrium: Bounded Rationality of LLMs and humans in Strategic Decision-making](https://mlsanity.com/paper/2506.09390/) (2025)
- [The Effect of State Representation on LLM Agent Behavior in Dynamic Routing Games](https://mlsanity.com/paper/2506.15624/) (2025)
- [Cattle Trade: A Multi-Agent Benchmark for LLM Bluffing, Bidding, and Bargaining](https://mlsanity.com/paper/2605.14537/) (2026)
- [Reliable agent engineering should integrate machine-compatible organizational principles](https://mlsanity.com/paper/2512.07665/) (2025)
- [Reasonably reasoning AI agents can avoid game-theoretic failures in zero-shot, provably](https://mlsanity.com/paper/2603.18563/) (2026)
- [Evaluating Large Language Models in a Complex Hidden Role Game](https://mlsanity.com/paper/2605.22826/) (2026)
- [A game theory for foundation models shows new paths to rational cooperation through similarity inference](https://mlsanity.com/paper/2608.03958/) (2026)
- [Assessing mentalization in humans and large language models](https://mlsanity.com/paper/2608.26291/) (2026)
- [Language Model Agents Under Attack: A Cross Model-Benchmark of Profit-Seeking Behaviors in Customer Service](https://mlsanity.com/paper/2512.24415/) (2025)
- [When Identity Overrides Incentives: Representational Choices as Governance Decisions in Multi-Agent LLM Systems](https://mlsanity.com/paper/2601.10102/) (2026)
- [LLM Agents Make Collective Belief Dynamics Programmable: Challenges and Research Directions](https://mlsanity.com/paper/2605.19915/) (2026)
- [From Blueprint to Reality: Modeling and Applying Putnam's Social Capital Theory with LLM-based Multi-agent Simulations](https://mlsanity.com/paper/2607.06080/) (2026)
- [Preference Reasoning under Indeterminacy in Large Language Models](https://mlsanity.com/paper/2608.18631/) (2026)
- [Benchmarking large language model agent societies against human behavioural distributions](https://mlsanity.com/paper/2608.28182/) (2026)
- [Choosing LLMs for Strategic Agent Interactions](https://mlsanity.com/paper/2610.18354/) (2026)

## Abstract (arXiv)

Strategic decision-making involves interactive reasoning where agents adapt their choices in response to others, yet existing evaluations of large language models (LLMs) often emphasize Nash Equilibrium (NE) approximation, overlooking the mechanisms driving their strategic choices. To bridge this gap, we introduce an evaluation framework grounded in behavioral game theory, disentangling reasoning capability from contextual effects. Testing 22 state-of-the-art LLMs, we find that GPT-o3-mini, GPT-o1, and DeepSeek-R1 dominate most games yet also demonstrate that the model scale alone does not determine performance. In terms of prompting enhancement, Chain-of-Thought (CoT) prompting is not universally effective, as it increases strategic reasoning only for models at certain levels while providing limited gains elsewhere. Additionally, we investigate the impact of encoded demographic features on the models, observing that certain assignments impact the decision-making pattern. For instance, GPT-4o shows stronger strategic reasoning with female traits than males, while Gemma assigns higher reasoning levels to heterosexual identities compared to other sexual orientations, indicating inherent biases. These findings underscore the need for ethical standards and contextual alignment to balance improved reasoning with fairness.