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

2025-12-08

AI Summary

This study investigates strategic intent recognition in large language models (LLMs) within multi-agent interactions. To address this, we extend the FAIRGAME framework by designing payoff-scaled Prisoner’s Dilemma and dynamic multi-agent Public Goods Game environments. Leveraging strategy classification models and behavioral trajectory analysis, we systematically evaluate LLMs’ cooperation versus defection tendencies in repeated social dilemmas. Our key findings reveal that linguistic formulation exerts influence on strategic choice comparable to architectural differences across models; LLMs exhibit pronounced incentive sensitivity, cross-lingual behavioral variation, endgame defection bias, and a systematic cooperation bias. These results provide empirical grounding and methodological tools for AI safety governance, design of multi-agent coordination mechanisms, and development of AI-driven social infrastructure.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Natural Language Processing: (Large) Language Models

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• Analyze LLM strategic behavior in repeated social dilemmas
• Identify systematic cooperation biases across models and languages
• Provide a foundation for auditing LLMs as strategic agents

Innovation

• Extending FAIRGAME framework for LLM evaluation
• Using payoff-scaled Prisoners Dilemma and Public Goods Game
• Training classifiers to interpret LLM strategic intentions