CORE: Measuring Multi-Agent LLM Interaction Quality under Game-Theoretic Pressures

TL;DR

This paper introduces CORE, a new metric for evaluating the quality of multi-agent LLM interactions across different game-theoretic settings, revealing how social incentives influence language use and diversity.

Contribution

The paper presents CORE, a novel, comprehensive metric that quantifies dialog quality in multi-agent LLM interactions, incorporating linguistic diversity and semantic coherence.

Findings

Cooperative interactions show higher vocabulary growth and more repetition.

Competitive interactions exhibit less vocabulary expansion and lower repetition.

CORE effectively measures linguistic robustness across various social settings.

Abstract

Game-theoretic interactions between agents with Large Language Models (LLMs) have revealed many emergent capabilities, yet the linguistic diversity of these interactions has not been sufficiently quantified. In this paper, we present the Conversational Robustness Evaluation Score: CORE, a metric to quantify the effectiveness of language use within multi-agent systems across different game-theoretic interactions. CORE integrates measures of cluster entropy, lexical repetition, and semantic similarity, providing a direct lens of dialog quality. We apply CORE to pairwise LLM dialogs across competitive, cooperative, and neutral settings, further grounding our analysis in Zipf's and Heaps' Laws to 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. These results provide new insights into how social incentives influence language adaptation, and highlight CORE as a robust diagnostic for measuring linguistic robustness in multi-agent LLM systems. Our code is available at https://github.com/psyonp/core.