Lexical Structure Under Game-Theoretic Pressures: Statistical Laws in Multi-Agent Communication

ACL ARR 2025 July Submission707 Authors

Abstract: Game-theoretic interactions between agents with Large Language Models (LLMs) have revealed many emergent capabilities, yet the lexical analysis of these interactions has not been sufficiently investigated. In this paper, we investigate how different game-theoretic interaction modes shape the statistical properties of emergent communication in multi-agent systems. Specifically, we simulate pairwise dialogs between LLMs and analyze their language output using Zipf's and Heaps' Laws, which characterize word frequency distributions and vocabulary growth. Our findings show that cooperative settings exhibit both steeper Zipf distributions and higher Heap exponents, indicating more repetition alongside greater vocabulary expansion. In contrast, competitive interactions display lower Zipf and Heaps exponents, reflecting less repetition and more constrained vocabularies. Additionally, we observe distinct patterns in unique and total token usage across interaction modes. These results provide new insights into how social incentives influence language adaptation, with implications for designing more effective multi-agent communication systems.

Paper Type: Long

Research Area: Linguistic theories, Cognitive Modeling and Psycholinguistics

Research Area Keywords: linguistic theories, lexical relationships, LLM agents, Game Theory, Zipf's Law, Heaps' Law

Contribution Types: NLP engineering experiment, Publicly available software and/or pre-trained models

Languages Studied: English

Reassignment Request Area Chair: This is not a resubmission

Reassignment Request Reviewers: This is not a resubmission

A1 Limitations Section: This paper has a limitations section.

A2 Potential Risks: Yes

A2 Elaboration: Ethics statement

B Use Or Create Scientific Artifacts: Yes

B1 Cite Creators Of Artifacts: Yes

B1 Elaboration: Section 4

B2 Discuss The License For Artifacts: No

B2 Elaboration: All models are publicly available under the MIT license and were publicly available during the time of experimentation.

B3 Artifact Use Consistent With Intended Use: N/A

B4 Data Contains Personally Identifying Info Or Offensive Content: Yes

B4 Elaboration: We clarify that all data has been screened for harmful content in the Ethics statement

B5 Documentation Of Artifacts: Yes

B5 Elaboration: Section 4, Appendix A

B6 Statistics For Data: Yes

B6 Elaboration: Section 4, Appendix A

C Computational Experiments: Yes

C1 Model Size And Budget: Yes

C1 Elaboration: Limitations

C2 Experimental Setup And Hyperparameters: Yes

C2 Elaboration: Appendix A

C3 Descriptive Statistics: Yes

C3 Elaboration: Section 5

C4 Parameters For Packages: Yes

C4 Elaboration: Section 4, Appendix A

D Human Subjects Including Annotators: No

D1 Instructions Given To Participants: N/A

D2 Recruitment And Payment: N/A

D3 Data Consent: N/A

D4 Ethics Review Board Approval: N/A

D5 Characteristics Of Annotators: N/A

E Ai Assistants In Research Or Writing: Yes

E1 Information About Use Of Ai Assistants: N/A

E1 Elaboration: Used AI to troubleshoot minor bugs in Python Code for visualizations and SLURM scripts.

Author Submission Checklist: yes

Submission Number: 707