# Understanding LLM Agent Behaviours via Game Theory: Strategy Recognition, Biases and Multi-Agent Dynamics

arXiv: https://arxiv.org/abs/2512.07462 · HTML: https://mlsanity.com/paper/2512.07462/

## Key facts

- Cited by 11 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 12 of its 34 references that are in the map.
- First posted on arXiv 8 Dec 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, 12 of 12)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [A Multitask, Multilingual, Multimodal Evaluation of ChatGPT on Reasoning, Hallucination, and Interactivity](https://mlsanity.com/paper/2302.04023/) (2023)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [Multi-Agent Risks from Advanced AI](https://mlsanity.com/paper/2502.14143/) (2025)
- [When to (or not to) trust intelligent machines: Insights from an evolutionary game theory analysis of trust in repeated games](https://mlsanity.com/paper/2007.11338/) (2020)
- [FAIRGAME: a Framework for AI Agents Bias Recognition using Game Theory](https://mlsanity.com/paper/2504.14325/) (2025)
- [Media and responsible AI governance: a game-theoretic and LLM analysis](https://mlsanity.com/paper/2503.09858/) (2025)
- [Do LLMs trust AI regulation? Emerging behaviour of game-theoretic LLM agents](https://mlsanity.com/paper/2504.08640/) (2025)
- [Inferring Strategies from Observations in Long Iterated Prisoner's Dilemma Experiments](https://mlsanity.com/paper/2202.04171/) (2022)
- [Strategic Communication and Language Bias in Multi-Agent LLM Coordination](https://mlsanity.com/paper/2508.00032/) (2025)
- [Can LLMs effectively provide game-theoretic-based scenarios for cybersecurity?](https://mlsanity.com/paper/2508.05670/) (2025)
- [Can Media Act as a Soft Regulator of Safe AI Development? A Game Theoretical Analysis](https://mlsanity.com/paper/2509.02650/) (2025)

## Built on by (most cited first, 11 of 11)

- [Self-Improvement of Large Language Models: A Technical Overview and Future Outlook](https://mlsanity.com/paper/2603.25681/) (2026)
- [RvB: Automating AI System Hardening via Iterative Red-Blue Games](https://mlsanity.com/paper/2601.19726/) (2026)
- [Three AI-agents walk into a bar . . . . `Lord of the Flies' tribalism emerges among smart AI-Agents](https://mlsanity.com/paper/2602.23093/) (2026)
- [Coalition Formation in LLM Agent Networks: Stability Analysis and Convergence Guarantees](https://mlsanity.com/paper/2604.14386/) (2026)
- [The Yerkes-Dodson Curve for AI Agents: Emergent Cooperation Under Environmental Pressure in Multi-Agent LLM Simulations](https://mlsanity.com/paper/2603.07360/) (2026)
- [Multi-Agent Strategic Games with LLMs](https://mlsanity.com/paper/2605.03604/) (2026)
- [Is Lying an Emergent Behaviour in LLMs? Evidence from Gaslighting AI agents in a Sustainability Game](https://mlsanity.com/paper/2606.28456/) (2026)
- [The Politician, the Liar, and the Obedient Worker: Emerging Behavior of LLM Agents in Hierarchical Games](https://mlsanity.com/paper/2608.09574/) (2026)
- [Preference Reasoning under Indeterminacy in Large Language Models](https://mlsanity.com/paper/2608.18631/) (2026)
- [Recursive Reasoning or Statistical Extrapolation? In-Context Learning in Multi-Agent Interdependent Decision-Making](https://mlsanity.com/paper/2609.18591/) (2026)
- [Fair Like Us? Auditing LLM Alignment in Resource Allocation](https://mlsanity.com/paper/2609.29692/) (2026)

## Abstract (arXiv)

As Large Language Models (LLMs) increasingly operate as autonomous decision-makers in interactive and multi-agent systems and human societies, understanding their strategic behaviour has profound implications for safety, coordination, and the design of AI-driven social and economic infrastructures. Assessing such behaviour requires methods that capture not only what LLMs output, but the underlying intentions that guide their decisions. In this work, we extend the FAIRGAME framework to systematically evaluate LLM behaviour in repeated social dilemmas through two complementary advances: a payoff-scaled Prisoners Dilemma isolating sensitivity to incentive magnitude, and an integrated multi-agent Public Goods Game with dynamic payoffs and multi-agent histories. These environments reveal consistent behavioural signatures across models and languages, including incentive-sensitive cooperation, cross-linguistic divergence and end-game alignment toward defection. To interpret these patterns, we train traditional supervised classification models on canonical repeated-game strategies and apply them to FAIRGAME trajectories, showing that LLMs exhibit systematic, model- and language-dependent behavioural intentions, with linguistic framing at times exerting effects as strong as architectural differences. Together, these findings provide a unified methodological foundation for auditing LLMs as strategic agents and reveal systematic cooperation biases with direct implications for AI governance, collective decision-making, and the design of safe multi-agent systems.