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Emergent Coordination in Multi-Agent Language Models

ICLR 2026 · Multi-agent systems and games › LLM agents · approach: LLM multi-agent decision making · 2 citations (OpenAlex)

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Applies a partial information decomposition of time-delayed mutual information to multi-agent LLM groups playing a binary-search guessing game, testing for dynamical emergence and how persona and theory-of-mind prompts steer synergy and differentiation.

Problem

Whether multi-agent LLM systems behave as integrated collectives with higher-order (synergistic) structure rather than mere aggregates of individual agents, and how prompt design affects this.

Approach

A data-driven information-theoretic framework using two-source partial information decomposition of time-delayed mutual information, a practical macro-signal criterion, and a triplet coalition test, combined with row- and column-shuffle surrogate nulls, applied to LLM groups under control, persona, and persona+theory-of-mind prompts.

Key results

• Bias-corrected practical emergence is above zero in all conditions (control p=1.5e-16; persona p=6.6e-7; ToM p=0.02).
• Only the ToM condition shows significant triplet mutual information I_3 (p=3.5e-14) and total stability (p=2.9e-14); control and persona are indistinguishable from zero.
• Redundancy and synergy interact significantly in predicting success (interaction beta=0.24, p=0.014); success rate did not differ significantly across interventions.

Surprising findings

• Success rate did not differ significantly across the control, persona, and ToM interventions despite large differences in coordination structure.
• Qwen3 reasoning model entered infinite chain-of-thought loops (paralysis under coordination ambiguity), and smaller Llama 8B largely failed to break oscillation.

Limitations

• Single minimalist task (group binary search), limiting generality across tasks.
• Entropy estimation is fragile with small samples; analyses restricted to order-2 synergy and two-bin discretization, with some results sensitive to bin count and null choice.
• Synergy and performance are endogenous to run length; the ToM mediation effect is only marginally significant (p=0.053).

Experimental setup

Benchmarks: group binary search (sum guessing) game

Metrics: success rate dynamical synergy (Syn) practical emergence score S_macro I_3 / total stability G_3 hierarchical model likelihood-ratio test

Baselines: control prompt condition persona prompt condition coordination-free functional null model

Builds on: Williams-Beer partial information decomposition time-delayed mutual information group binary search task

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