# When Numbers Start Talking: Numerical Signalling and Strategic Behaviour Among LLMs

arXiv: https://arxiv.org/abs/2610.03033 · HTML: https://mlsanity.com/paper/2610.03033/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 51 references that are in the map.
- First posted on arXiv 2 Oct 2026.

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

- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [Emergent Multi-Agent Communication in the Deep Learning Era](https://mlsanity.com/paper/2006.02419/) (2020)
- [AI Agents vs. Agentic AI: A Conceptual Taxonomy, Applications and Challenges](https://mlsanity.com/paper/2505.10468/) (2025)
- [Multi-Agent Risks from Advanced AI](https://mlsanity.com/paper/2502.14143/) (2025)
- [From LLM Reasoning to Autonomous AI Agents: A Comprehensive Review](https://mlsanity.com/paper/2504.19678/) (2025)
- [Emergence of Language with Multi-agent Games: Learning to Communicate with Sequences of Symbols](https://mlsanity.com/paper/1705.11192/) (2017)
- [Emergent social conventions and collective bias in LLM populations](https://mlsanity.com/paper/2410.08948/) (2024)
- [Secret Collusion among AI Agents: Multi-Agent Deception via Steganography](https://mlsanity.com/paper/2402.07510/) (2024)
- [How Well Can LLMs Negotiate? NegotiationArena Platform and Analysis](https://mlsanity.com/paper/2402.05863/) (2024)
- [Embodied LLM Agents Learn to Cooperate in Organized Teams](https://mlsanity.com/paper/2403.12482/) (2024)
- [Covert Malicious Finetuning: Challenges in Safeguarding LLM Adaptation](https://mlsanity.com/paper/2406.20053/) (2024)
- [Latent Collaboration in Multi-Agent Systems](https://mlsanity.com/paper/2511.20639/) (2025)
- [Preventing Language Models From Hiding Their Reasoning](https://mlsanity.com/paper/2310.18512/) (2023)
- [Nicer Than Humans: How do Large Language Models Behave in the Prisoner's Dilemma?](https://mlsanity.com/paper/2406.13605/) (2024)
- [Hidden in Plain Text: Emergence & Mitigation of Steganographic Collusion in LLMs](https://mlsanity.com/paper/2410.03768/) (2024)
- [TwinMarket: A Scalable Behavioral and Social Simulation for Financial Markets](https://mlsanity.com/paper/2502.01506/) (2025)
- [Will Systems of LLM Agents Cooperate: An Investigation into a Social Dilemma](https://mlsanity.com/paper/2501.16173/) (2025)
- [FAIRGAME: a Framework for AI Agents Bias Recognition using Game Theory](https://mlsanity.com/paper/2504.14325/) (2025)
- [Towards Mechanistic Interpretability of Graph Transformers via Attention Graphs](https://mlsanity.com/paper/2502.12352/) (2025)
- [Generative AI for Game Theory-based Mobile Networking](https://mlsanity.com/paper/2404.09699/) (2024)
- [Media and responsible AI governance: a game-theoretic and LLM analysis](https://mlsanity.com/paper/2503.09858/) (2025)
- [Surprising gender biases in GPT](https://mlsanity.com/paper/2407.06003/) (2024)
- [CoMet: Metaphor-Driven Covert Communication for Multi-Agent Language Games](https://mlsanity.com/paper/2505.18218/) (2025)
- [Strategic Communication and Language Bias in Multi-Agent LLM Coordination](https://mlsanity.com/paper/2508.00032/) (2025)
- [Social physics in the age of artificial intelligence](https://mlsanity.com/paper/2603.16900/) (2026)
- [Inducing Personality in LLM-Based Honeypot Agents: Measuring the Effect on Human-Like Agenda Generation](https://mlsanity.com/paper/2503.19752/) (2025)
- [Can LLMs effectively provide game-theoretic-based scenarios for cybersecurity?](https://mlsanity.com/paper/2508.05670/) (2025)
- [The Illusion of Rationality: Tacit Bias and Strategic Dominance in Frontier LLM Negotiation Games](https://mlsanity.com/paper/2512.09254/) (2025)

## Abstract (arXiv)

Large language model (LLM)-based agents increasingly operate in multi-agent systems (MAS) characterised by strategic interaction. However, little is known about whether, and to what extent, different types of messages affect the outcomes of strategic games. By investigating AI agents based on four popular LLMs, playing four games with different cooperation equilibria, we study whether messages of different kinds (natural language, numerical signals, or random sequences) significantly modify the levels of cooperation in each game, also depending on the agents' assigned personalities. We observe that structured messages alter the final payoffs for most games and LLMs, but without a predictable pattern; this challenges the assumption that AI agents can converge to stable equilibria regardless of additional capabilities. Moreover, we observe that agent-generated numerical messages depart from randomness, most strongly and consistently when agents are explicitly instructed to communicate; however, they introduce an additional interpretability challenge, as their symbol distributions are mostly associated with the payoff structure and typically become more concentrated with repetition, but are overall difficult for humans to interpret. Monitoring for coordination of AI agents through restricted channels should thus prioritise message-level fingerprints, which generalise across models, over behavioural decisions, which do not.