Emergent Coordination in Multi-Agent Language Models

TL;DR

This paper introduces an information-theoretic framework to detect and analyze higher-order emergent structures in multi-agent language models, demonstrating how prompt design can steer collective behavior.

Contribution

It develops a data-driven method using partial information decomposition to identify and localize emergence in multi-agent LLM systems, distinguishing genuine synergy from spurious correlations.

Findings

Groups with personas show identity-linked differentiation and goal-directed complementarity.

The framework is robust across different measures and not explained by simple coordination or dynamics.

Prompt design can steer systems from mere aggregation to higher-order collective behavior.

Abstract

When are multi-agent LLM systems merely a collection of individual agents versus an integrated collective with higher-order structure? We introduce an information-theoretic framework to test -- in a purely data-driven way -- whether multi-agent systems show signs of higher-order structure. This information decomposition lets us measure whether dynamical emergence is present in multi-agent LLM systems, localize it, and distinguish spurious temporal coupling from performance-relevant cross-agent synergy. We implement a practical criterion and an emergence capacity criterion operationalized as partial information decomposition of time-delayed mutual information (TDMI). We apply our framework to experiments using a simple guessing game without direct agent communication and minimal group-level feedback with three randomized interventions. Groups in the control condition exhibit strong temporal synergy but little coordinated alignment across agents. Assigning a persona to each agent introduces stable identity-linked differentiation. Combining personas with an instruction to ``think about what other agents might do'' shows identity-linked differentiation and goal-directed complementarity across agents. Taken together, our framework establishes that multi-agent LLM systems can be steered with prompt design from mere aggregates to higher-order collectives. Our results are robust across emergence measures and entropy estimators, and not explained by coordination-free baselines or temporal dynamics alone. Without attributing human-like cognition to the agents, the patterns of interaction we observe mirror well-established principles of collective intelligence in human groups: effective performance requires both alignment on shared objectives and complementary contributions across members.