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When Numbers Start Talking: Implicit Numerical Coordination Among LLM-Based Agents

Alessio Buscemi, Daniele Proverbio, Alessandro Di Stefano, The Anh Han, German Castignani, Pietro Liò

TL;DR

This work investigates covert, implicit signaling among LLM-driven agents in four canonical two-player games using a structured, multi-condition experimental framework. By comparing explicit language, absence of communication, and various numerical signaling regimes (decimal, hexadecimal, random, and externally injected), the study reveals that covert signals exhibit low entropy and context-dependent effects on coordination, particularly in games with strategic uncertainty. Repeated interactions amplify signaling tendencies in restricted numerical spaces (decimal) while preserving dispersion in hex representations, and correlations with natural-language baselines indicate partial alignment rather than full replication of language-based coordination. The findings highlight the need to evaluate multi-agent LLM systems through both outcome metrics and the structure of inter-agent communication, with implications for designing robust and interpretable coordination mechanisms.

Abstract

LLMs-based agents increasingly operate in multi-agent environments where strategic interaction and coordination are required. While existing work has largely focused on individual agents or on interacting agents sharing explicit communication, less is known about how interacting agents coordinate implicitly. In particular, agents may engage in covert communication, relying on indirect or non-linguistic signals embedded in their actions rather than on explicit messages. This paper presents a game-theoretic study of covert communication in LLM-driven multi-agent systems. We analyse interactions across four canonical game-theoretic settings under different communication regimes, including explicit, restricted, and absent communication. Considering heterogeneous agent personalities and both one-shot and repeated games, we characterise when covert signals emerge and how they shape coordination and strategic outcomes.

When Numbers Start Talking: Implicit Numerical Coordination Among LLM-Based Agents

TL;DR

This work investigates covert, implicit signaling among LLM-driven agents in four canonical two-player games using a structured, multi-condition experimental framework. By comparing explicit language, absence of communication, and various numerical signaling regimes (decimal, hexadecimal, random, and externally injected), the study reveals that covert signals exhibit low entropy and context-dependent effects on coordination, particularly in games with strategic uncertainty. Repeated interactions amplify signaling tendencies in restricted numerical spaces (decimal) while preserving dispersion in hex representations, and correlations with natural-language baselines indicate partial alignment rather than full replication of language-based coordination. The findings highlight the need to evaluate multi-agent LLM systems through both outcome metrics and the structure of inter-agent communication, with implications for designing robust and interpretable coordination mechanisms.

Abstract

LLMs-based agents increasingly operate in multi-agent environments where strategic interaction and coordination are required. While existing work has largely focused on individual agents or on interacting agents sharing explicit communication, less is known about how interacting agents coordinate implicitly. In particular, agents may engage in covert communication, relying on indirect or non-linguistic signals embedded in their actions rather than on explicit messages. This paper presents a game-theoretic study of covert communication in LLM-driven multi-agent systems. We analyse interactions across four canonical game-theoretic settings under different communication regimes, including explicit, restricted, and absent communication. Considering heterogeneous agent personalities and both one-shot and repeated games, we characterise when covert signals emerge and how they shape coordination and strategic outcomes.
Paper Structure (12 sections, 1 figure, 4 tables)

This paper contains 12 sections, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Games Selection
  4. LLM Selection
  5. Types of Communication
  6. Implementation
  7. Experimental setting
  8. Results
  9. Communication randomness and structure
  10. One-shot games
  11. Repeated games
  12. Conclusion

Figures (1)

  • Figure 1: Mean cooperation (pure Cooperation = 1, pure Defection = 0) by communication type (axes of the radar plot, see Tab. \ref{['tab:communication']} for legend) and personality combinations (color-coded) across the four games (H, SD, SH, PD).