Do Agent Societies Develop Intellectual Elites? The Hidden Power Laws of Collective Cognition in LLM Multi-Agent Systems

Kavana Venkatesh; Jiaming Cui

cs.MAApr 3, 2026

Do Agent Societies Develop Intellectual Elites? The Hidden Power Laws of Collective Cognition in LLM Multi-Agent Systems

Authors: Kavana Venkatesh, Jiaming Cui

Organizations: Department of Computer Science, Virginia Tech, Blacksburg, VA

Abstract

Large Language Model (LLM) multi-agent systems are increasingly deployed as interacting agent societies, yet scaling these systems often yields diminishing or unstable returns, the causes of which remain poorly understood. We present the first large-scale empirical study of coordination dynamics in LLM-based multi-agent systems, introducing an atomic event-level formulation that reconstructs reasoning as cascades of coordination. Analyzing over 1.5 Million interactions across tasks, topologies, and scales, we uncover three coupled laws: coordination follows heavy-tailed cascades, concentrates via preferential attachment into intellectual elites, and produces increasingly frequent extreme events as system size grows. We show that these effects are coupled through a single structural mechanism: an integration bottleneck, in which coordination expansion scales with system size while consolidation does not, producing large but weakly integrated reasoning processes. To test this mechanism, we introduce Deficit-Triggered Integration (DTI), which selectively increases integration under imbalance. DTI improves performance precisely where coordination fails, without suppressing large-scale reasoning. Together, our results establish quantitative laws of collective cognition and identify coordination structure as a fundamental, previously unmeasured axis for understanding and improving scalable multi-agent intelligence.

Figures & tables

Figure 1: Heavy-tailed coordination cascades across observables. CCDFs show a power-law regime (

2<\hat{\alpha}<3

) with truncation at large

x

. Dashed lines indicate MLE fits above

x_{\min}

. Truncated power laws are favored over log-normal and exponential alternatives (Table 2 ).

Panel of Table 1 — Table 1: Primitive coordination events used in our analysis. An event is a single coordination step in the reasoning process (e.g., delegation, revision, contradiction, or merge). Events are linked through claim and subtask relationships, and each row defines a quantity computed over these events rather than over entire tasks. Legend: Root Claim Propagation Claims Critique Claim Merge Claim .

	Tail statistics							Model comparison
Observable	$n_{\text{total}}$	$x_{\min}$	$n_{\text{tail}}$	$\hat{\alpha}$	Tail family	$x_{\max}$	Distinct	LR (TPL vs LN)	$p$	LR (TPL vs PL)	$p$
Delegation cascade	342,300	5	92,400	2.28	Trunc. PL	118	103	+4.6	0.002	+2.8	0.009
Revision wave	344,300	4	134,300	2.41	Trunc. PL	74	61	+3.8	0.005	+1.7	0.037
Contradiction burst	255,300	4	56,200	2.16	Trunc. PL	83	73	+4.2	0.004	+0.9	0.020
Merge fan-in	278,500	3	39,000	2.71	Trunc. PL	33	27	+3.9	0.006	+3.3	0.001
Total Cognitive Effort (TCE)	411,300	8	123,400	2.22	Trunc. PL	1320	1203	+5.1	0.001	+2.8	0.012

Table 2: Global tail statistics and model comparisons. Tail behavior is summarized by

\hat{\alpha}

(MLE above

x_{\min}

) and distinct tail values. Positive likelihood ratios favor TPL over LN and PL. * Lower

p

indicates stronger support for TPL.

Figure 2: Finite-size stability of heavy-tailed coordination dynamics. (Left) Estimated tail exponents

\hat{\alpha}

(MLE) vs. agent count

N

. Estimates fluctuate at small

N

due to limited tail samples, then stabilize and converge beyond

N\approx 64

, indicating emergence of a consistent heavy-tailed regime. (Right) Mean maximum event size

\langle x_{\max}\rangle

vs.

N

. The upper tail grows systematically across observables, with strongest expansion for TCE, showing that increasing system size expands the reachable coordination tail.

Chain

Star

Hierarchical

Mesh

Observable

Task

\hat{\alpha}

\hat{x}_{c}

LR T/LN

LR T/PL

\hat{\alpha}

\hat{x}_{c}

LR T/LN

LR T/PL

\hat{\alpha}

\hat{x}_{c}

LR T/LN

LR T/PL

\hat{\alpha}

\hat{x}_{c}

LR T/LN

LR T/PL

Delegation

Coding

2.46

+4.0

+2.5

2.30

+4.3

+2.7

2.36

+4.2

+2.6

2.16

+4.6

+2.8

2.64

+3.7

+2.3

2.48

+3.9

+2.5

2.54

+3.8

+2.4

2.34

+4.2

+2.6

Planning

2.24

+4.5

+2.8

2.08

+4.9

+3.0

2.14

+4.8

+2.9

1.94

+5.3

+3.2

Reasoning

2.34

+4.3

+2.7

2.18

+4.7

+2.8

2.24

+4.5

+2.8

2.04

+5.0

+3.0

Merge Fan-In

Coding

2.89

+3.3

+3.0

2.73

+3.6

+3.2

2.79

+3.5

+3.1

2.59

+3.9

+3.3

Table 3: Tail heterogeneity across task types and communication topologies. For each observable and task–topology condition, we report the fitted truncated power-law exponent

\hat{\alpha}

, cutoff parameter

\hat{x}_{c}

, and log-likelihood ratios LR T/LN and LR T/PL comparing the truncated power law (TPL) against the log-normal (LN) and pure power-law (PL) alternatives, respectively. Lower

\hat{\alpha}

and larger

\hat{x}_{c}

indicate broader, less sharply truncated coordination tails. Planning and reasoning tasks consistently exhibit heavier tails than coding and QA across all topology conditions, and denser topologies (mesh, star) support longer-lived cascades than locally connected structures (chain), with the planning

\times

mesh combination producing the heaviest tails in every observable.

Figure 3: Topology- and task-specific heavy-tailed coordination cascades in multi-agent LLM systems. Complementary cumulative distribution functions (CCDF) of coordination-event sizes

P(X\geq x)

across four coordination observables: Delegation Cascade , Revision Wave , Contradiction Burst , and Total Coordination Effort (TCE) under four agent interaction topologies ( Chain , Star , Hierarchical , and Dynamic Reputation ) and four task families ( Reasoning , Coding , QA , and Coordination ). Each curve represents the empirical distribution of coordination-event sizes for a given task family within a topology. Across all settings, the distributions exhibit broad heavy-tailed behavior with estimated scaling exponents

2<\hat{\alpha}<3

in the intermediate regime (values shown per panel), consistent with scale-free coordination dynamics. While the precise tail exponent varies modestly across tasks and architectures, the heavy-tailed form persists across all topologies, indicating that complex coordination in LLM multi-agent systems produces heterogeneous cascades spanning multiple scales. Deviations at the largest event sizes reflect finite-size truncation due to system constraints such as limited agent attention, bounded communication bandwidth, and task decomposition depth.

Figure 4: Scale-dependent emergence of broad elite tiers. (a) (a) Top-

k

active agents (

E^{\mathrm{active}}_{10}

E^{\mathrm{active}}_{25}

E^{\mathrm{active}}_{50}

) capture disproportionate shares of coordination effort relative to egalitarian baselines;

E^{\mathrm{all}}_{10}

(dashed) confirms the result is not driven by inactive agents. of coordination effort relative to egalitarian baselines. (b) Excess concentration

\Delta^{\mathrm{active}}_{k}

above equal participation increases with

N

, with strongest gains in the top decile and quartile. (c) Cumulative concentration curves vs

N

increasingly bow above the equality line, indicating broader and more dominant elite tiers at scale.

Figure 5: Preferential attachment is a core micro-mechanism behind heavy-tailed coordination and elite concentration in LLM agent societies. (a) The routing ratio

R(x,N)

rises above the null baseline once a claim accumulates prior engagement, and the effect strengthens with system size

N

, revealing scale-dependent preferential amplification before saturating in the tail. (b) Estimated attachment slopes

\hat{\beta}

vary systematically across topology and task type, with stronger reinforcement in star, fully connected, and modular societies than in tree or chain settings. (c) Event types differ in cascade-sustaining power: delegation and contradiction occupy the high-amplification, high-continuation region, while revision is intermediate and merge fan-in remains comparatively local. (d) Conditions with larger condition-level attachment slope

\hat{\beta}

also exhibit larger top-10% effort share

E^{\mathrm{active}}_{10}

, linking local reinforcement directly to macro-level elite concentration.

Figure 6: Conflict-integration dynamics and performance degradation in the high-intensity regime. (a) Mean task success across coordination intensity regimes reveals a non-monotonic signature: performance plateaus at moderate intensity before undergoing significant degradation in the high-intensity tail. This decline is strongly correlated with an elevated contradiction burden and a concomitant collapse in merge conversion efficiency. The vertical dashed line demarcates the transition from productive coordination to the conflict-dominated regime. (b1) Outcome distribution among high-intensity tasks, illustrating a distinct skew toward failure as coordination complexity increases. (b2) Decomposition of elite contribution shares in high-intensity regimes. Successful runs maintain higher integration capacity, whereas unsuccessful runs are characterized by an increased share of contradictory interactions and diminished merge contributions, suggesting that systemic failure is driven by an inability to resolve dense coordination conflicts.

M

denotes the merge-event share of total elite coordination effort.

Figure 7: Extreme-value scaling of coordination cascades. Mean maximum event size

\langle x_{\max}\rangle

vs. agent count

N

(log–log). Solid curves show empirical values with 95% CIs; dashed lines denote power-law fits (

\hat{\gamma}

). All observables scale with

N

, with TCE showing the strongest growth and closest alignment to EVT predictions (

\hat{\gamma}_{\text{TCE}}\approx 0.85

vs.

\gamma_{\text{th}}\approx 0.82

), indicating systematic expansion of the coordination tail.

Figure 8: Deficit-Triggered Integration (DTI) in coordination cascades. A cascade initially expands through parallel revision, contradiction, and delegation branches, leading to increasing fragmentation (left). DTI monitors this imbalance and triggers integration when it exceeds a threshold, consolidating active branch heads into a unified representation (middle). The cascade then resumes from this integrated state, enabling continued exploration with improved coherence and reduced fragmentation (right).

Figure 9: Impact of Deficit-Triggered Integration (DTI) on collective cognition dynamics. (a) DTI preserves the heavy-tailed structure of coordination cascades while shifting truncation earlier, reducing excess tail mass without altering the intermediate scaling regime. Fixed-interval intervention, in contrast, introduces premature truncation and distorts the tail. (b) The growth of extreme coordination events with system size is preserved under DTI, but large cascades are systematically attenuated, leading to more controlled scaling behavior. (c) DTI reduces the concentration of cognitive effort among top agents, moderating elite dominance while maintaining a non-uniform and productive coordination structure. DTI converts late-stage expansion into earlier integration, yielding more stable and balanced collective reasoning without disrupting the underlying heavy-tailed organization of agent coordination.

Figure 10: Heterogeneity of DTI gains across topology and task family. Relative improvement in task success (%) under DTI versus baseline, reported per topology-task condition. Gains range from +2.07% (QA $\times$ Chain) to +12.34% (Planning $\times$ Mesh/FC). DTI produces the largest improvements in conditions exhibiting the strongest expansion-integration imbalance in baseline coordination dynamics. Row and column marginals show topology- and task-level averages.

Appendix figures & tables32 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 11: Internal composition of claim-level coordination cascades and the scale-conditioned integration bottleneck. (a) Claim-rooted cascades are grouped by total cognitive effort (TCE) quantile, pooling all tasks, topologies, and agent scales. As cascades move into the far tail, their internal event composition shifts toward delegation and contradiction , while merge remains comparatively weak and increasingly subproportional; revision plays an intermediate role. (b) The same bottleneck appears in the merge conversion ratio across both cascade size and society scale: integration is strongest for smaller cascades in smaller societies and weakens progressively toward extreme cascades in larger societies. Together, these results show that large coordination cascades are increasingly expansion-heavy and merge-poor, and that this integration deficit strengthens with scale.

Symbol	Meaning
$X$	Random variable representing an event-size observable
$x$	Realized value of $X$
$P(X\geq x)$	Complementary cumulative distribution function (CCDF) of $X$
$\alpha$	Tail exponent of the power-law / truncated power-law model
$\hat{\alpha}$	MLE estimate of $\alpha$
$x_{\min}$	Lower cutoff above which tail fitting is performed

Appendix

Table 4: Notation for heavy-tail modeling and model comparison (H1).

Symbol	Meaning
$\mathrm{TCE}(c_{r})$	Total Cognitive Effort: total number of downstream events from root claim $c_{r}$
$S_{k}(c_{r})$	Top- $k$ contribution share within cascade $\mathcal{C}_{r}$
$E^{\mathrm{active}}_{k}$	Top- $k$ % effort share; denominator = active agents only
$E^{\mathrm{all}}_{k}$	Top- $k$ % effort share; denominator = all $N$ agents
$\Delta^{\mathrm{active}}_{k}$	Excess share above egalitarian baseline $k/N$
$S_{p}$	Cumulative concentration curve (Lorenz-style)

Appendix

Table 5: Notation for elite concentration and inequality (H2).

Symbol	Meaning
$x_{\max}(N)$	Maximum cascade size in a system of $N$ agents
$\langle x_{\max}\rangle$	Expected maximum event size (averaged over runs)
$\hat{\gamma}$	Empirically estimated extreme-value scaling exponent
$\gamma_{\mathrm{th}}=1/(\alpha-1)$	Theoretical EVT prediction for scaling exponent

Appendix

Table 6: Notation for extreme-event scaling (H3).

Symbol	Meaning
$R(x,N)$	Routing ratio: relative likelihood a claim with activity $x$ is selected
$\beta$	Reinforcement strength in the routing rule (Eq. 6 )
$\hat{\beta}(N)$	Empirical condition-level attachment slope
$\hat{\beta}_{e}$	Event-specific attachment slope
$\hat{\beta}_{c}$	Contradiction scaling exponent used in DTI pressure model
$p_{\mathrm{cont},e}$	Continuation probability per event type

Appendix

Table 7: Notation for preferential attachment and Deficit-Triggered Integration (DTI).

t_{r}\leftarrow 0,\qquad M_{r}\leftarrow 0

Appendix

Algorithm 1 Deficit-Triggered Integration (DTI)

Observable	$\hat{\alpha}$	CI	$n_{\text{tail}}/n$	KS
Delegation	2.28	[2.24, 2.32]	0.27	0.042
Revision	2.41	[2.36, 2.46]	0.31	0.047
Contradiction	2.16	[2.11, 2.21]	0.22	0.039
Merge	2.71	[2.63, 2.79]	0.14	0.051
TCE	2.22	[2.18, 2.26]	0.30	0.035

Appendix

Table 8: Robustness of heavy-tail fits across observables. Confidence intervals are obtained via bootstrap resampling.

$N$	Top-1	Top-10%	Gini	$N_{\text{eff}}/N$
8	0.04	0.17	0.20	0.88
32	0.07	0.21	0.25	0.81
128	0.08	0.23	0.31	0.73
512	0.11	0.29	0.39	0.64

Appendix

Table 9: Concentration of reasoning effort across agent scales. Top-

k

shares increase while the effective number of contributing agents decreases with

N

Metric	Mean	Std (across seeds)
Gini	0.37	0.018
Top-10% share	0.29	0.017
$N_{\text{eff}}/N$	0.64	0.015

Appendix

Table 10: Stability of inequality metrics across random seeds (averaged over all conditions).

Percentile	Delegation	Contradiction	Merge	Merge ratio
Median	0.30	0.21	0.19	0.37
90th	0.36	0.26	0.15	0.24
99th	0.41	0.31	0.11	0.15
Top 1%	0.45	0.34	0.08	0.10

Appendix

Table 11: Event composition across cascade size percentiles. Expansion dominates the tail while merge activity diminishes, revealing an integration bottleneck.

Benchmark	Seeds	Expanded tasks	Avg. dependencies
GAIA	30	150	2.1
SWE-bench	30	150	2.4
REALM	11	55	2.0
MultiAgentBench	30	150	2.3

Appendix

Table 12: Statistics of the task expansion module. Event structure is not injected but emerges from agent interaction during execution.

Claim Type	Description
Proposed Claim	An initial statement or solution generated by an agent.
Revised Claim	A modification of a prior claim that refines or corrects it.
Contradictory Claim	A claim that challenges or disputes an existing claim.
Merged Claim	A claim produced by combining multiple parent claims.

Appendix

Table 13: Types of claims observed in coordination traces. Claims represent reasoning artifacts that are created and transformed through events.

Panel of Figure 12 — Figure 12: Hierarchy of coordination structures in a multi-agent system. A task defines the global objective, which is decomposed into subtasks; subtasks produce claims; and claims evolve through event-level coordination steps. Our analysis operates on these events rather than on whole tasks.

Event Type	Operation on Claims	Resulting Structure
revise_claim	single parent $\rightarrow$ child	chain
contradict_claim	parent $\rightarrow$ multiple children	branching
merge_claims	multiple parents $\rightarrow$ child	multi-parent (DAG)
delegate_subtask	creates new subtask context	hierarchical tree

Appendix

Table 14: Event types and their induced transformations on the claim structure. These operations define how the claim graph evolves from chains to branching structures and ultimately to a directed acyclic graph through merge operations.

Panel of Figure 13 — Figure 13: Event-induced transformations of the claim structure. Revision produces linear chains, contradiction introduces branching around a claim, and merge combines multiple parent claims into a single node, yielding a directed acyclic graph.

Panel of Figure 14 — Figure 14: Delegation and cascade structure. Delegation events construct a subtask tree (left), defining how work is decomposed. Coordination cascades (right) capture the total downstream activity triggered by a root claim, combining revision, contradiction, and merge dynamics. Total Cognitive Effort (TCE) is defined as the size of this reachable cascade.

Field	Description
run_id	Identifier for the experiment run
step_id	Temporal ordering of events
agent_id	Acting agent
event_type	Type of coordination event
target_claim_id	Referenced claim (if applicable)
target_subtask_id	Referenced subtask (if applicable)

Appendix

Table 15: Event-level fields recorded for each coordination step.

Field	Description
claim_id	Unique identifier for each claim
parent_claim_ids	Parent claims defining DAG edges
root_claim_id	Root ancestor of the claim
claim_depth	Depth within the claim DAG
claim_status	Proposed, revised, contradictory, or merged

Appendix

Table 16: Fields defining the claim-level DAG structure.

Field	Description
subtask_id	Unique identifier for each subtask
parent_subtask_id	Parent subtask in hierarchy
subtask_depth	Depth in subtask tree
assigned_agent	Responsible agent
subtask_status	Active or completed

Appendix

Table 17: Fields defining the hierarchical subtask decomposition.

Field	Description
revision_chain_id	Groups claims in a revision sequence
contradiction_group_id	Groups claims targeting the same parent claim
merge_id	Identifier for merge operations
merge_parent_ids	Parent claims involved in merge

Appendix

Table 18: Derived fields used to group events into coordination structures.

Panel of Figure 15 — Figure 15: From structured event traces to coordination cascades. Logged event fields define parent–child claim relationships, from which we reconstruct the claim DAG. Cascades are then extracted as root-centered reachable subgraphs, enabling computation of event-level observables such as revision waves, contradiction bursts, merge fan-in, and total cognitive effort.

Panel of Figure 16 — Figure 16: End-to-end coordination pipeline in our experimental setup. Left: task expansion produces an interdependent task tree with cross-subtask dependencies. Center: agent interactions generate claims and event-induced edges, forming a claim DAG. Right: the cascade extracted from the root claim captures the full coordination effort used to compute event-level observables.

Observable	Trigger Condition	Structure	Output
Delegation Cascade	Subtree rooted at a delegate_subtask event	Subtask tree	Node count
Revision Wave	Maximal chain of claims with identical revision_chain_id	Claim DAG	Length
Contradiction Burst	Claims referencing the same parent claim within a temporal window $\tau$	Claim DAG + timestamps	Count
Merge Fan-in	Number of parent_claim_ids in a merge_claims event	Claim DAG	In-degree
Total Cognitive Effort (TCE)	Reachable subgraph from root_claim_id	Cascade	Size

Appendix

Table 19: Formal trigger conditions for coordination observables. Each observable is computed from structured traces via deterministic extraction rules applied to reconstructed coordination structures.

	Tail structure			LR tests		Pref. Reinf.	Concentration		Outcome
Model	$\hat{\alpha}$	$\hat{x}_{c}$	$x_{\max}$	$\mathrm{LR}_{\mathrm{T}/\mathrm{LN}}$	$\mathrm{LR}_{\mathrm{T}/\mathrm{PL}}$	$\hat{\beta}$	$E^{\mathrm{all}}_{10}$	Active	Task Succ.
GPT-4o-mini	2.22	57	1320	+5.2	+2.8	0.16	25%	81%	0.48
Qwen 2.5 72B	2.27	44	1035	+5.0	+2.7	0.15	23%	79%	0.43
Llama 3.1 70B	2.34	30	1012	+4.8	+2.5	0.13	19%	78%	0.41
Qwen 2.5 7B	2.74	9	440	+3.5	+1.7	0.07	14%	72%	0.27

Appendix

Table 20: Global pooled TCE robustness across models. All 16 topology

\times

task conditions are pooled per model. For all cross-model TCE fits, we fix the tail onset threshold at

x_{\min}=8

to maintain a common fitting regime across models. Tail statistics report the fitted truncated-power-law parameters for total collective effort (TCE), together with likelihood-ratio comparisons against log-normal and pure power-law alternatives. Preferential reinforcement is summarized by

\hat{\beta}

, concentration by the top-10% effort share and active-agent fraction, and outcome by overall task success.

		Tail structure		LR tests		Concentration	Outcome
Topology	Model	$\hat{\alpha}$	$\hat{x}_{c}$	$\mathrm{LR}_{\mathrm{T}/\mathrm{LN}}$	$\mathrm{LR}_{\mathrm{T}/\mathrm{PL}}$	$E^{\mathrm{all}}_{10}$	Task succ.
Chain	GPT-4o-mini	2.49	23	+4.6	+2.6	17%	0.43
	Qwen 2.5 72B	2.52	21	+4.5	+2.5	16%	0.40
	Llama 3.1 70B	2.61	18	+4.2	+2.3	14%	0.36
	Qwen 2.5 7B	2.88	9	+3.0	+1.5	11%	0.19
Star	GPT-4o-mini	2.21	44	+5.2	+2.8	32%	0.47

Appendix

Table 21: TCE heavy-tail structure by topology and model. Results are pooled across task types within each topology. For all cross-model TCE fits, we fix the tail onset threshold at

x_{\min}=8

Figure 17: Coordination-law flower signatures across models. Each panel summarizes one model using five global event observables: delegation cascade, revision wave, contradiction burst, merge fan-in, and total cognitive effort (TCE). Petal extent jointly reflects four law dimensions: heavier tails (lower

\hat{\alpha}

), larger truncation scale

\hat{x}_{c}

, stronger preferential reinforcement

\hat{\beta}

, and greater elite concentration

E^{\mathrm{all}}_{10}

. Across all four models, the qualitative ordering is preserved: TCE remains the strongest composite coordination signal, delegation and contradiction form the next tier of broad coordination, revision is intermediate, and merge is the weakest and most localized. Moving from GPT-4o-mini to Qwen 2.5 72B, Llama 3.1 70B, and Qwen 2.5 7B, the petals contract inward rather than changing shape abruptly, indicating that heavy-tailed coordination and elite formation persist across model families and scales, but with shorter tails, lower cutoff scales, and weaker concentration in smaller models owing to reduced model-inherent resources.

		Tail structure		LR tests		Concentration	Outcome
Task type	Model	$\hat{\alpha}$	$\hat{x}_{c}$	$\mathrm{LR}_{\mathrm{T}/\mathrm{LN}}$	$\mathrm{LR}_{\mathrm{T}/\mathrm{PL}}$	$E^{\mathrm{all}}_{10}$	Task succ.
Planning	GPT-4o-mini	2.11	54	+5.2	+2.2	30%	0.45
	Qwen 2.5 72B	2.14	50	+5.1	+2.1	27%	0.41
	Llama 3.1 70B	2.23	44	+4.8	+1.9	22%	0.40
	Qwen 2.5 7B	2.53	14	+3.6	+1.1	16%	0.23
Reasoning	GPT-4o-mini	2.20	45	+5.2	+2.7	23%	0.56

Appendix

Table 22: TCE heavy-tail structure by task type and model. Results are shown for four representative task families and are pooled across topologies, seeds, and agent-society sizes within each task-type

\times

model condition. For all cross-model TCE fits, we fix the tail onset threshold at

x_{\min}=8

E^{\mathrm{all}}_{10}

, and outcome by pooled task success.

Component	Configuration
Benchmarks	GAIA, SWE-bench Verified, REALM-Bench, MultiAgentBench
Task types	QA, reasoning, coding, planning
Total tasks	$\sim$ 400 (stratified across benchmarks and difficulty levels)
Agent counts ( $N$ )	$\{8,16,32,64,128,256,512\}$
Topologies	Chain, Star, Tree, Hierarchical, Fully Connected, Sparse Mesh, Dynamic Reputation
Agent model	Shared LLM (GPT-4o-mini)

Appendix

Table 23: Experimental configuration summary.

Observable	Samples	Mean/run
Delegation cascades	$\sim 3.0\times 10^{5}$	$\sim 3.1$
Revision waves	$\sim 2.8\times 10^{5}$	$\sim 2.9$
Contradiction bursts	$\sim 3.2\times 10^{5}$	$\sim 3.3$
Merge events	$\sim 2.5\times 10^{5}$	$\sim 2.6$
TCE (root cascades)	$\sim 1.7\times 10^{5}$	$\sim 1.7$
Total	$\mathbf{>1.5\times 10^{6}}$	$\mathbf{\sim 15.3}$

Appendix

Table 24: Coordination-event samples extracted from

\sim 98{,}000

runs. Each run produces multiple event instances depending on the realized interaction trace.

Figure 18: Workload-expansion validation across agent society size. (a) Active-agent fraction

A(N)

for four task families remains high across scales, staying above 80% even at

N=512

, indicating sustained participation. (b) Agents per subtask induced by the expansion rule, compared to the target scaling

N/\lceil N^{0.65}\rceil

. The gradual increase from

\sim

2 to

\sim

9 agents per subtask shows that workload grows with

N

without over-concentrating agents. Together, these results verify that the expansion module maintains balanced workload and broad agent utilization while not prescribing coordination structure.

Component	Configuration
Orchestration	LangGraph (uniform routing, state, and execution)
Base prompt	Task, neighbors, structured history
Topology addendum	Topology-specific routing behavior (chain, star, tree, hierarchical, mesh, reputation)
Task addendum	Benchmark-specific instructions (QA, coding, planning, reasoning)
Tool access	Restricted to benchmark-native tools
Context budget	4000-token window

Appendix

Table 25: Standardized agent configuration used across all experiments.

Benchmark	Task type	Approx. tasks	Difficulty
GAIA	QA / multimodal reasoning	$\sim$ 150	Medium–Hard
SWE-bench Verified	Code debugging / patching	$\sim$ 235	Hard
REALM-Bench	Planning / constraint reasoning	$\sim$ 14	Hard
MultiAgentBench	Coordination / interaction tasks	$\sim$ 6 scenarios	Variable

Appendix

Table 26: Benchmarks used for workload generation and evaluation.

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Mar 3, 2026

Benchmarking Emergent Coordination in Large-Scale LLM Populations: An Evaluation Framework on the MoltBook Archive

As multi-agent Large Language Model (LLM) systems scale, evaluating their emergent coordination dynamics becomes increasingly critical. However, current evaluation paradigms-focused on single agents or small, explicitly structured groups-fail to capture the self-organization and viral information dynamics that arise in large, decentralized populations. We introduce a systematic evaluation framework to benchmark role specialization, information diffusion, and cooperative task resolution in open agent environments. We demonstrate this framework on the MoltBook Observatory Archive, a dataset of 2.73M interactions among 90,704 autonomous agents, establishing quantitative baselines for emergent coordination. Our evaluation reveals a pronounced core-periphery structure (silhouette 0.91), heavy-tailed cascade distributions (

α= 2.57

), and severe coordination overhead in decentralized task resolution (Cohen's

d = -0.88

against a single-agent baseline). By providing standardized evaluation tasks and empirical baselines, our framework enables the rigorous comparison of future multi-agent protocols and establishes evaluation itself as an object of scientific study.

Brandon Yee, Pairie Koh

Management Lab, Yee Collins Research Group

Multi-Agent Coordination LLM Agent Evaluation Emergent Behavior in Multi-Agent Systems AI Agent Benchmarks

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Sep 27, 2026

Collective Regimes in Multi-Agent LLMs under Reasoning Effort and Communication Topology

Multi-agent LLM systems are increasingly used for deliberation and evaluation, often under the assumption that greater peer interaction leads to more reliable consensus. Existing work largely evaluates these systems through final accuracy or aggregate agreement. However, such measures do not reveal how agreement is organized in the panel. In this paper, we study N = 50 stateless LLM agents that update their predictions from locally visible peers, and characterize their behavior using both global and local measurements of agreement. We identify three collective regimes: synchronised, twisted (locally ordered but globally incoherent) and chimera-like, where coherent and incoherent subpopulations coexist. Increasing reasoning effort in gpt-5-mini shifts panels from variable, often fragmented outcomes toward locally ordered twisted states, and a small follow-up shows such states can also form from permuted initial conditions, whereas increasing communication connectivity drives them toward global synchronisation. Fragmentation collapses faster as algebraic connectivity increases across rewired graphs. The topology effect also appears on a non-circular judging task and across models from three providers. Finally, low spatial heterogeneity does not guarantee global consensus: 40% of trials with Delta Z below 0.03 retain a twisted configuration through the final 20 turns. These results show that reasoning effort and communication topology control different aspects of multi-agent coordination, and that aggregate agreement alone is insufficient to characterize collective LLM behavior.

Machiko Hirota, Akshara Nadayanur Sathis Kanna, Ujwal Kumar +1

University of Pennsylvania · Carnegie Mellon University · Shibaura Institute of Technology

Multi-Agent LLM Systems Multi-Agent Coordination Multi-Agent Consensus Emergent Behavior in Multi-Agent Systems Multi-Agent Communication

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