TeamGym: A Gym for Team Decision-Making by AI Agents with Distributed Information

Motivation and contribution

• TeamGym addresses gaps left by individual-agent benchmarks and multi-agent harnesses, which provide limited evidence about agents’ retrieval and communication abilities or how teams respond to information and communication conditions.The paper motivates team evaluation because collective intelligence in human groups is linked to social sensitivity and turn-taking and predicts team performance better than individual intelligence.Source: §1 · p. 2

Method

• TeamGym identifies pivotal information units by checking that candidate evidence jointly supports the reference decision and that removing any unit leaves it unsupported or unresolved.The instances are constructed from real-world corpora and may use corpus-provided reference decisions or decisions built from annotations and source materials.Source: §1 · p. 2
• Holding an instance and its pivotal information fixed, TeamGym varies who initially holds the information, whether it is provided directly or embedded in source material, communication structure, and token budgets.These controls support evaluation and training of participant and coordinator policies.Source: §1 · p. 2
• TeamGym’s source corpora cover contracts, regulations, SEC filings, biomedical papers, and source code, with finite-choice, written, and numeric decision formats.The corpora span four domains.Source: §1 · p. 3, Table 1 · p. 3

Findings

• Across 8 language models and 12 source corpora, distributing the same pivotal information across participants lowers success by 22.9 percentage points, with source-material retrieval lowering it by a further 19.9 points.The comparisons hold the problem instance and pivotal information fixed; TeamGym also finds communication-structure differences vary across distribution conditions.Source: §1 · p. 3

Team decision theory and organizational economics

• Classical team decision theory studies cooperative decision makers with shared objectives and decentralized information, but largely analyzes computation structures and policies rather than how to learn and implement them computationally.TeamGym evaluates and trains language-model policies and compares policy collections before and after training under the same conditions.Source: §2 · pp. 3–4

Mechanism design

• Mechanism-design models may assume private information can be elicited directly, whereas TeamGym studies bounded natural-language messages derived from source material.The paper notes that attention and cognitive limits constrain agents’ ability to identify, extract, and communicate information in long source material.Source: §2 · p. 4

Communication constraints

• Where some communication research idealizes nonbinding observation and message resources, TeamGym makes resource budgets explicit..Source: §2 · p. 4

Scope

• The paper defers related work on multistage communication, human-AI and group decision making, multi-agent LLM systems, benchmark contrasts, and source corpora to Section 6.Source: §2 · p. 4

3.1. Decision Problem and Communication

• A team decision instance fixes source materials, an objective, decision format, possible decisions, and an evaluator; policies act on role-permitted queries, messages, or decisions under decentralized observations and resource budgets.Evaluation uses expected team payoff, and changing communication conditions need not change the underlying instance.Source: §3.1 · p. 4
• The five communication structures differ in speaker selection and coordinator control, and in who makes the final decision.Round robin, Current-speaker selection, and Simultaneous responses use a separate final decision maker; Coordinator-selected speaker and Broadcast query give the coordinator control and the final decision.Source: §3.1 · p. 5, Figure 2 · p. 5

3.2. Problem-Instance Construction and Evaluation

• Pivotal information is an inclusion-minimal set of units sufficient for a highest-payoff decision, with each unit necessary in the sense that removing it leaves insufficient information to guarantee that decision.DeepSWE instead uses functional PIUs validated under a fixed, bounded protocol.Source: §3.2 · p. 5
• Candidate evidence units are grounded in source materials and checked for joint sufficiency and leave-one-out necessity before being retained as pivotal information.The resulting pivotal information can then be allocated across participants while preserving the decision task and reference decision.Source: §3.2 · p. 6, Figure 3 · p. 6
• PIU distributions vary who initially holds each unit while keeping the pivotal information and reference decision unchanged; source-material conditions distribute units without dividing a PIU and check that no participant can decide correctly alone.Not every instance admits every distribution condition, and success is assessed using problem-specific evaluators, reference decisions, LLM judges, or repository verification.Source: §3.2 · pp. 6–7

4.1. Problem Instances

• Table 2 summarizes problem-instance counts across four domains and twelve source corpora; GPT-5.5 given all pivotal information succeeded at least once on every evaluated instance.This check verifies that a model with all pivotal information could solve each instance before that information was distributed.Source: §4.1 · p. 8, Table 2 · p. 8

4.2. Cross-Domain Communication and Retrieval Gaps

• Across all four domains, substantial communication and retrieval gaps show that strong individual performance does not by itself predict effective teamwork.Single-Agent All-PIU measures individual performance with all pivotal information available; it does not predict how well a model communicates, integrates, or retrieves distributed pivotal information.Source: §4.2 · p. 9

4.3. Mechanisms Linking Communication Structure to Episode Success

• Correct synthesis increases success in all four conditions, while its effect is smaller when GPT-5.5 replaces the participant model as final decision maker.Removing error uptake has a statistically significant effect only for Qwen3-235B participants, and that effect is smaller than the correct-synthesis effect in every condition.Source: §4.3 · p. 10

4.4. PIU-Distribution and Communication-Structure Interaction

• Communication-structure effects depend on PIU distribution across 11 problem families in both PIU-Only and Full-Context conditions (p < .001 for each interaction test).The analysis does not estimate how much of the cross-domain interaction either of the examined mechanisms explains.Source: §4.4 · pp. 10–11

4.4.1. Example 1: Narrow coordinator queries limit the PIUs communicated by one participant.

• Adding PIU-category labels and reporting instructions reduces the finance interaction from +15.5 to +5.9 points; removing the coordinator query changes it to −5.4 points without additions and −9.3 with them.All three changes from the original-query replay are statistically significant, while none of the resulting interactions is significant; the interventions support a role for query content but do not establish a zero residual interaction.Source: §4.4.1 · p. 11

4.4.2. Example 2: Messages from participants assigned no PIU impair the final decision.

• With source material only for participants assigned no PIU, success under All-but-one PIU concentration and simultaneous responses falls from 69.7% to 22.5%.Source material only for participants assigned PIUs reduces success to 54.8%; source placement changes both processing and messages, so it does not isolate their effects.Source: §4.4.2 · p. 12
• Removing messages from participants assigned no PIU improves success when those participants receive source material, but not significantly when they do not.The interaction between source-material access and message removal is significant; the test does not distinguish transcript length from distracting or contradictory content.Source: §4.5 · p. 12

4.5. Token-Budget Effects

• Increasing the budget from 32 to 128 tokens raises the rate from 55.3% to 78.6%, averaged over private-note budgets, with no further gain at 256 tokens.Private-note differences are smaller, and larger local-transcript budgets show no consistent improvement on Multi-LexSum.Source: §4.5 · p. 13

5.1.1. Two-Stage Policy Training

• On 36 CUAD validation instances, two-stage training raises the LLM-judged score from 12.14% to 16.84% after participant-only training and to 23.33% after coordinator-only continuation.The validation gains do not transfer to the 26 held-out MAUD-derived instances; the stages can alter participant messages, coordinator queries, and final decisions.Source: §5.1.1 · p. 13

5.1.2. Joint Two-Policy Training

• Under joint two-policy training, the CUAD validation score rises from 11.97% to 22.38%, and the share of instances where every participant is queried rises from 80.6% to 100%.Querying every participant is not part of the reward; the learned behavior also includes shorter queries and no copying of the problem question in the first query.Source: §5.1.2 · pp. 13–14
• On 26 MAUD-derived instances, the score changes only from 5.12% to 5.58%, while every participant is queried and sends a public message in all 26 trained-policy episodes.Under the base policies, every participant sends a public message in 20 instances; coordination behavior transfers even when final-decision quality changes little.Source: §5.1.2 · p. 14

5.2. Current-speaker selection: Training a Shared Participant Policy

• Under current-speaker selection, cross-replay attributes a 6.95-point gain on 40 instances to replacing the base communication trajectory with the trained trajectory, averaged across final-decision policies.Replacing the base final-decision policy with the trained policy does not significantly improve scores; training also changes participation and next-speaker selection behaviors that are not rewarded directly.Source: §5.2 · p. 15
• On FinDVer, trained communication transcripts improve performance by 12.6 points under the same final-decision policy and increase the share of PIUs in transcripts by 15.9 points.On held-out FinLongDocQA, changes under the same final-decision policy and in transcript PIU share are not statistically distinguishable from zero, despite improved end-to-end score and completion.Source: §5.2 · p. 15

5. Policy Training with TeamGym: Emergent Coordination

• Each of the two policy-training demonstrations reports one training run; results across additional runs and base models remain to be evaluated.Source: §5.2 · p. 16

• Human-group research motivates studying interaction and finite resource constraints, but TeamGym evaluates neither human-AI teams nor token budgets as models of human cognition.Source: §6 · p. 16
• Unlike multi-agent systems and benchmarks that study collaboration or coordination, TeamGym controls source-grounded pivotal-information distribution and whether participants receive facts directly or must retrieve them from source material.Unlike multi-agent debate, TeamGym gives participants different initial local observations rather than the same problem.Source: §6 · p. 16
• TeamGym’s unit of analysis is a team whose decision-relevant evidence is divided among participants, unlike collaborative-gym work focused on a user or simulator collaborating with one LLM agent.Source: §6 · p. 16

7. Conclusion

• Across 8 language models and 12 source corpora, distributing the same pivotal information across participants lowers episode success by 22.9 percentage points, and requiring retrieval from source material lowers it by a further 19.9 points.Communication structures also vary in effectiveness across pivotal-information distribution conditions.Source: §7 · p. 17
• Across two fixed communication structures, policy training improves final-decision quality and induces emergent coordination in participation, speaker selection, and communication.With coordinator control, joint training produces a compact information-elicitation protocol; without a coordinator, training improves quality and completion while increasing participation. Increased participation makes more pivotal information available on FinDVer validation, but not held-out FinLongDocQA.Source: §7 · p. 17
• The training demonstrations use one run each, and Coordinator-selected-speaker improvements are measured on CUAD-derived validation instances used for checkpoint selection.The conclusion describes future extensions including strategic information transmission, unreliable participants, partially aligned objectives, and explicit retrieval costs.Source: §7 · p. 17

Reproducibility Statement

• The supplementary archive is described as providing materials needed to reproduce the reported construction, evaluation, analysis, and training results; the authors also report using AI assistants in research and manuscript work.The authors say they reviewed AI-generated outputs and approved the final scientific claims.Source: Reproducibility Statement · p. 17, Use of AI Assistants · p. 18

A. Deferred Table for Section 5.2: Communication-Trajectory Analysis

• Table 10 compares communication trajectories for base and trained policies.The caption specifies that all entries are percentages.Source: Table 10 · p. 25
• The “Same final-decision policy” measure is the LLM-judged score from applying one common GPT-5.5 final-decision policy to every communication transcript.Source: Table 10 · p. 25

B. Closest Benchmark Comparisons

• HiddenBench evaluates 65 Hidden Profile instances and 15 models, while TeamGym varies source-grounded information and interaction conditions with the underlying problem and evidence requirements fixed.HiddenBench examines whether directly presented participant-specific facts enter public discussion and improve group voting [Li et al., 2025, 2026].Source: B. Closest Benchmark Comparisons · p. 25
• SILO-BENCH studies synthetic distributed-computation problems with programmatically known answers and weak-scaling evaluations from 2 to 100 agents [Zhang et al., 2026].Its design examines how organization, consensus, and communication cost change as team size and the global problem grow.Source: B. Closest Benchmark Comparisons · p. 25
• TeamGym’s communication and retrieval gaps compare Single-Agent All-PIU with Multi-Agent PIU-Only, and Multi-Agent PIU-Only with Multi-Agent Full-Context, respectively.These outcome-based contrasts differ from SILO-BENCH’s log-based Communication-Reasoning Gap; TeamGym studies performance on fixed, source-grounded decisions while varying pivotal-information distribution and communication structures.Source: B. Closest Benchmark Comparisons · pp. 25–26

C. Communication-Structure Implementation and Relation to Prior Work

• Communication policies receive structure-permitted observations and produce role-specific actions; the five structures draw on deliberation, mediated communication, and speaker-selection research but are not exhaustive.Invalid or omitted next-speaker choices under Current-speaker selection default to the next participant in fixed cyclic order.Source: C. Communication-Structure… · p. 26

D.1. Decision Sufficiency and Pivotal Information

• A pivotal-information set is sufficient when its information identifies a decision optimal across admissible instances, and each unit is pivotal if removing it removes that guarantee.The construction procedure operationalizes the complete-set and leave-one-out conditions using annotations, reference reasoning, grounding, and model-based checks; the minimal set need not be unique.Source: §D.1 · p. 27

D.2. General Construction Procedure

• Construction retains source units necessary to support required answer components or reasoning steps, using sequential removal checks when the retained reasoning does not establish necessity.A model-based check first requires the reference decision, then tests whether uncertainty remains after removing each candidate unit; released code also provides this check when necessity is established from reasoning.Source: §D.2 · pp. 27–28
• PIUs are assigned before non-PIU source units are distributed, and participant descriptions indicate likely information holders without revealing their PIUs’ content or conclusions.Distribution may account for PIU proximity and balance observation lengths; checks preserve assigned PIUs under truncation and avoid splitting PIUs across source units.Source: §D.2 · p. 28, §D.3.5 · p. 34

D.3.2. Problem Instances and PIU Distributions in the Legal Evaluation

• The legal evaluation crosses 163 retained problem instances with three conditions and uses 514 PIU distributions across five distribution conditions and five communication structures.The same 163 legal instances are evaluated in each of the three conditions; Table 12 summarizes instance and distribution statistics, with source-material lengths reflecting the 40,000-token observation budget.Source: §D.3.2 · p. 30, Table 12 · p. 30, §D.3.3 · p. 30

D.3.4. CUAD Problem-Instance Construction

• CUAD instances combine two to five positive annotated spans into finite-choice legal decisions, retaining 538 instances from 289 contracts after checks.Each instance must have a unique reference decision and at least two PIUs; the source contract is divided into contiguous units without splitting PIUs.Source: §D.3.4 · pp. 31–32

D.3.5. MAUD Problem-Instance Construction

• MAUD construction produces 557 retained instances from 100 agreements, combining multiple provision excerpts into a finite-choice decision rather than treating row-level annotations as PIUs.Provision excerpts are located in agreements, and the agreements are divided into contiguous units that preserve PIUs; retained instances contain at least two PIUs from one agreement and category.Source: §D.3.5 · pp. 33–34

D.3.6. eCFR Casebook Problem-Instance Construction

• eCFR Casebook construction retains 18 of 20 candidate instances and evaluates short compliance conclusions against required regulatory, factual, threshold, and action components.Instances use regulatory text from 12 C.F.R. Parts 1 and 3 and controlled transaction memos (Office of the Federal Register, 2026a,b,c).Source: §D.3.6 · p. 34
• eCFR construction selects regulatory provisions dependent on multiple conditions and retains instances with five to seven PIUs.Candidate units combine eCFR regulatory text with transaction facts from the memo; a model-based check determines which units form Imin_q.Source: §D.3.6 · p. 34
• eCFR participants receive long source excerpts that preserve assigned PIUs and remove those assigned to others, targeting 12,000 tokens per participant.Across retained instances, source lengths range from 9,846 to 11,830 tokens.Source: §D.3.6 · p. 34
• eCFR instances require each PIU to appear in source material and in the initial observation of assigned participants, but not unassigned participants, and must pass centralized-PIU solvability checks.Instances failing any construction check are rejected.Source: §D.3.6 · p. 35

D.3.7. MSLR Problem-Instance Construction

• MSLR retains 11 of 100 candidate instances from 1,389 Chinese administrative-enforcement case files, requiring one target party, source material, and a final judgment.The legal evaluation uses all 11 retained instances.Source: §D.3.7 · p. 35
• MSLR (Yu et al., 2027) instances require a short enforcement conclusion covering information and timing, knowledge or access, trading, legal characterization, and final handling.The reference decision draws its final administrative handling from the judgment, and an evaluator compares free-form decisions against the reference and its answer components.Source: §D.3.7 · p. 35
• MSLR instances contain six exact, nonoverlapping case-file excerpts covering event and timing, knowledge or access, trading, legal characterization, and final handling.Each participant receives the complete anonymized case file with assigned PIU excerpts retained and unassigned PIU excerpts removed; instances must pass a centralized-PIU solvability check.Source: §D.3.7 · p. 35

D.3.8. Multi-LexSum Problem-Instance Construction

• Multi-LexSum retains 29 litigation instances with eight to twelve PIUs each, asking for determinate procedural or legal conclusions based on original documents rather than summaries.Questions omit collection-identifying names and identifiers; construction also requires source-grounded PIUs and reference decisions and solvability when all PIUs are centralized.Source: §D.3.8 · pp. 35–36
• Mean adjacent cosine similarity rose from .449 to .598 under maximum-similarity PIU ordering, but the exploratory comparison did not establish a difference between distributions.The paired LLM-judged-score difference was 6.7 percentage points, with a problem-instance-bootstrap 95% confidence interval of [−3.1, 16.3] percentage points; the comparison used the same 29 instances and changed only which PIUs occupied the distribution positions.Source: §D.3.8 · pp. 36–37, Table 16 · p. 37
• 30.7 percentage points: permuting participant descriptions lowered the mean LLM-judged score; the score fell in 24 instances, rose in three, and was unchanged in two (p = 4.9 × 10−5).Every PIU appeared in the communication transcript in all 29 instances with descriptions matched to assigned PIUs, versus 18 of 29 after permutation; the analysis isolates description assignment under Coordinator-selected speaker.Source: §D.3.8 · pp. 37–38, Table 17 · p. 38

D.3.9. SARA Problem-Instance Construction

• SARA retains 45 of 100 cases after solvability checks, with 393 PIUs and six to twelve per instance; tasks target a numeric intermediate conclusion and require a concise derivation.Five centralized-PIU solvability checks are run, and an instance is retained when at least four succeed; participant source material excludes calculation and reasoning steps used in construction.Source: §D.3.9 · pp. 38–39

D.4.1. Common Finance Construction Procedure

• Finance construction covers FinDVer and FinLongDocQA, using one SEC filing or company-year report per instance and source-grounded candidate units tied to answer components.Candidate units are complete paragraphs, tables, or adjacent label-value pairs; source material is checked for content that could reconstruct another participant’s assigned PIU.Source: §D.4 · p. 39, §D.4.1 · pp. 39–40

D.4.2. Problem Instances and PIU Distributions in the Finance Evaluation

• The finance evaluation uses 30 fixed instances from each corpus, with each instance assigned the One PIU per participant condition in both team conditions.For each policy, the conditions contain 90 FinDVer episodes and 90 FinLongDocQA episodes; deterministic subsets include 20 Form 10-K and 10 Form 10-Q filings, and 2022–2024 reports in the stated year-stratified counts.Source: §D.4.2 · p. 40

D.4.3. Finance Problem-Instance and PIU-Distribution Statistics

• Across 60 finance evaluation instances, FinDVer has 231 answer components across 70 source questions, while FinLongDocQA has 64 components across 63 questions.No participant initially receives every PIU; final decisions are graded on problem-specific criteria including values, units, periods, signs, scopes, calculations, and qualifying conclusions.Source: §D.4.3 · pp. 41–42

D.4.4. FinDVer Problem-Instance Construction

• FinDVer construction produces 389 filing-review instances from testmini, asking for related filing-specific findings, calculations, comparisons, or classifications rather than reusing original questions.The finance evaluation uses a fixed 30-instance subset; hidden annotations link answer components to PIUs and specify numeric criteria such as value, unit, sign, period, and tolerance.Source: §D.4.4 · pp. 42–43
• FinDVer candidate instances must pass source-grounding checks for calculations, comparisons, scope, and PIU-to-answer links, and their PIUs must suffice for a correct decision without redundancy.Instances are rejected if public information without PIUs is sufficient or if the common finance checks fail.Source: §D.4.4 · p. 43

D.4.5. FinLongDocQA Problem-Instance Construction

• FinLongDocQA construction creates report-specific memo or review tasks, links evidence units to claims, and requires every PIU to be necessary; participant packets are checked to prevent reconstruction of others’ PIUs.The construction uses 249 instances, while the finance evaluation uses a fixed 30-instance subset. Participants receive finance-specific reviewer labels that do not disclose PIU values or conclusions.Source: §D.4.5 · pp. 43–44

D.5.1. Common Medical Construction Procedure

• Medical construction derives free-response tasks from one source record, validates PIUs through grounded all-PIU and leave-one-out checks, and removes material that could reveal another participant’s PIUs.EvidenceBench uses one biomedical paper; MLCR uses one case, which may contain multiple visit summaries. Medical tasks preserve clinical scope and other claim-level details, and instances are retained only after applicable checks pass.Source: §D.5.1 · p. 45

D.5.2. Problem Instances and PIU Distributions in the Medical Evaluation

• 29 MLCR and 45 EvidenceBench instances form the medical evaluation; across 74 instances, every PIU has a source location and no team-evaluation participant initially receives every PIU.Each policy has 87 MLCR episodes and 135 EvidenceBench episodes across the three conditions. Figure 10 describes PIU and distribution statistics, while Table 25 summarizes means for 74 instances and 321 distributions.Source: §D.5.2 · pp. 45–46, §D.5.3 · p. 46, Figure 10 · p. 47

D.5.4. MLCR Problem-Instance Construction

• MLCR maps source questions to exact evidence atoms, forms clinically coherent tasks, and retains a PIU only when its removal breaks a supported claim; packet checks detect and remove foreign-PIU leakage.Evidence spans remain contiguous within a source document, with adjacent atoms included only to preserve needed context. Generic medical knowledge cannot replace missing patient-specific evidence.Source: §D.5.4 · p. 48

D.5.5. EvidenceBench Problem-Instance Construction

• EvidenceBench preserves each annotated sentence as a separate candidate unit, links units to answer components, and validates relevance, grounding, necessity, and PIU removal before distribution.At least two annotated sentences and two retained units are required; retained units remain separate even when they jointly support one answer component.Source: §D.5.5 · pp. 49–50
• EvidenceBench assigns each PIU’s source sentence to its owner and checks complete local observations for foreign-PIU reconstruction, deleting removable passages or rejecting instances when leakage persists.An exact duplicate, paraphrase, equivalent result, or combination of passages can count as reconstruction; shared topics or plausible inferences requiring outside knowledge do not.Source: §D.5.5 · p. 50

D.6.1. Source Corpora and Evaluation Scope

• Software-engineering construction fixes a repository and base commit, uses source-grounded PIUs assigned to participants, and withholds reference answers and hidden qualification records.The evaluation includes all 32 retained SWE Atlas instances across three conditions; DeepSWE uses a frozen 12-task cohort selected from 21 screened candidates to preserve language coverage and difficulty variation.Source: §D.6.1 · p. 51

D.6.2. Software-Engineering Problem-Instance Statistics

• Structural statistics cover 32 SWE Atlas one-each instances and 157 valid distributions, while DeepSWE statistics use its fixed 12-task cohort and functional one-each allocations.Tasks outside the DeepSWE cohort are excluded from the descriptive statistics.Source: §D.6.2 · p. 51, Figure 11 · p. 52, Table 27 · p. 52

D.6.3. SWE Atlas Codebase QnA Problem-Instance Construction

• For SWE Atlas, 32 of 124 official entries were retained, with candidate evidence grouped into at least two PIUs per collaborative instance and checked for sufficiency and leave-one-out necessity.Evidence collection includes exact source, test, and, when needed, runtime evidence; checks require the full set to support all criteria, the no-unit condition to fail, and each removal to fail its linked answer component.Source: §D.6.3 · pp. 52–53

D.6.4. DeepSWE Problem-Instance Construction

• DeepSWE PIUs represent functional behaviors required by the verifier, and their complete set supports a passing repair under a restricted five-turn protocol.Construction uses base-repository code and reproducible runtime evidence rather than reference-patch fragments; targeted leave-one-out checks diagnose PIU contributions but do not prove necessity across every possible repair procedure.Source: §D.6.4 · pp. 53–55

D.7. Independent Validation of PIU Construction

• The independent audit found the strongest evidence for individual PIU pivotality in leave-one-out checks; no participant observation sufficed for a complete FinLongDocQA decision, while two MAUD instances did.The audit covered 20 instances from each fixed 30-instance evaluation set and was targeted validation, not revalidation of every retained instance or corpus; unclear, invalid, failed, or missing judgments counted as non-passing.Source: §D.7 · pp. 55–56

E. Evaluation Results Across Domains and Source Corpora

• The cross-corpus comparisons use the same instances, pivotal information, and problem-specific evaluator across conditions, with One PIU per participant and 15 coordinator-selected responses before each final decision.Within each model–corpus comparison, the two multi-agent conditions hold PIU distribution, communication structure, and resource budgets fixed; confirmed context-window failures count as unsuccessful episodes, while infrastructure failures are unavailable.Source: E. Evaluation Results Across Domains… · p. 56

E.1. Source-Corpus Results

• Table 29 reports episode success rates for each source corpus, giving equal weight to models.Figure 6 pools problem instances across source corpora within each model.Source: §E.1 · p. 56

Model and source-corpus results

• For SWE Atlas Codebase QnA with GPT-5.5, the reported values are 84.4 ± 6.4 and 61.9 ± 10.6.The supplied row does not identify the condition labels for these two values.Source: Table 29 · p. 57, §E.2 · p. 59

Legal structured-interface failures

• 280 legal-evaluation episodes had structured-interface failures, 254 of them produced by the two Claude models.250 occurred during participant interaction and four at the final-decision stage.Source: §E.2 · p. 60

Evaluation caveat

• The failure archive retains only the first 500 characters of failed responses, preventing reliable semantic rescoring or distinguishing schema errors from truncation.It also omits complete raw responses, provider finish reasons, and output-token counts.Source: §E.2 · p. 60

Legal evaluation diagnostics

• Among valid final decisions, diagnostic success rates are 75.5%, 55.0%, and 35.1%, with communication and retrieval gaps of 20.5 and 19.9 points.These conditional rates are descriptive, not alternative end-to-end estimates, because producing a valid decision can depend on the model and evaluation condition.Source: §E.2 · p. 60, Table 31 · p. 60

Legal sensitivity analysis

• Excluding both Claude models, strict legal episode success rates are 69.8%, 49.4%, and 32.3%, with gaps of 20.4 and 17.1 percentage points.The corresponding conditional rates are 69.8%, 49.7%, and 33.0%, with gaps of 20.1 and 16.7 points.Source: §E.2 · p. 60

Legal evaluation diagnostics

• Legal Single-Agent Full-Context episode success counts final-decision structured-interface failures as unsuccessful, while serving-context rejections and other evaluation errors are excluded.Claude Sonnet 4.5 and Haiku 4.5 had seven and two such final-decision failures, respectively.Source: Table 30 · p. 57, §E.2 · p. 60

E.3. Single-Agent Full-Context Evaluation Counts

• 2,099 of 2,632 scheduled Single-Agent Full-Context inputs were evaluated; 460 exceeded a context window and 50 had output failures.Together with 23 other unavailable failures, 2,149 inputs contribute to episode-success estimates; output failures count as unsuccessful, while context-window and other unavailable failures are excluded.Source: §E.3 · pp. 61–62, Table 32 · p. 61

E.4.2. Correct-Synthesis Intervention

• Adding correct synthesis improves episode success in all four comparisons, with larger effects for Qwen3 than GPT-5.5 final decision makers.The synthesis claims exclude explicit answer proposals, so the effect cannot be attributed to direct answer copying.Source: §E.4.2 · p. 63, Table 33 · p. 63

E.4.3. Error-Uptake Intervention

• Removing error-uptake sentences improves success for Qwen3-235B-A22B participants under both final decision makers; Qwen3-32B estimates have confidence intervals including zero.Effects are smaller than the corresponding correct-synthesis effects, and the intervention is not applied to simultaneous responses because participants cannot observe one another.Source: §E.4.3 · p. 63, Table 34 · p. 63

E.4.4. Explicit Answer Proposals

• Removing explicit answer proposals has effects of −5.7 points for Qwen3-32B participants and final decision makers and −10.8 points for Qwen3-235B-A22B.The proposals also help Qwen3 final decision makers, but cannot explain the correct-synthesis result because those proposals are excluded from the synthesis set.Source: §E.4.4 · pp. 63–64

E.5. PIU-Distribution–Communication-Structure Interaction Estimates

• Table 35 presents PIU-distribution–communication-structure interaction estimates in episode-success percentage points, relative to One PIU per participant and Coordinator-selected speaker.Yellow cells and asterisks mark 95% confidence intervals excluding zero.Source: Table 35 · p. 64, §E.5 · p. 64

E.6. Robustness Analysis with Problem-Instance Fixed Effects

• With problem-instance fixed effects, the same five positive PIU-Only and two negative Full-Context interactions have confidence intervals excluding zero as in the main analysis.Point estimates are similar; one positive Full-Context interaction becomes significant, while one negative PIU-Only interaction no longer excludes zero.Source: §E.6 · p. 65, Table 36 · p. 65

E.7. Interpreting PIU-Distribution–Communication-Structure Interactions

• The finance interventions change coordinator query content while keeping speaker selection fixed, testing whether broader evidence requests help more when one participant holds multiple PIUs.The source materials, resource budgets, and final-decision procedure are held fixed; replayed effects apply to the recorded speaker sequence, not adaptive later selections or queries.Source: §E.7 · p. 65, §E.7.1 · p. 66

E.7.1. Finance: Design and Query Interventions

• The finance interaction I(k) subtracts the coordinator-condition PIU-distribution gap from the Round-robin gap; a selective coordinator improvement reduces I(k).The fixed Round-robin gap is −12.7 points.Source: §E.7.1 · p. 67

E.7.2. Finance: Results and Process Evidence

• The Round-robin-fixed communication-structure interaction is +15.5 points under the original-query replay; intervention changes are −9.6, −20.9, and −24.9 points.All three changes exclude zero, while their residual interaction intervals include zero; this does not establish equivalence to zero or reverse the communication-structure ordering.Source: §E.7.2 · p. 68, Table 38 · p. 69
• +23.9 points in FinDVer and +17.8 in FinLongDocQA: query removal improves success more under All-but-one PIU concentration without additions.With additions, the corresponding interactions are +16.7 points in FinDVer and +13.8 in FinLongDocQA; all four reported 95% confidence intervals exclude zero.Source: §E.7.2 · p. 70
• Without additions, the pooled-Qwen3 allocation gap falls from 28.2 points with original queries to 7.3 with the coordinator query removed; with additions, it falls from 18.6 to 3.4 points.These point estimates represent 74% and 82% attenuation of the respective original-query allocation gaps, not proportions of the communication interaction explained; residual intervals include zero but do not establish equivalence.Source: §E.7.2 · p. 70
• +6.3 points (95% CI [4.0, 8.8]): labels and instructions selectively increase substantive communication under All-but-one PIU concentration versus One PIU per participant.The corresponding complete-communication interaction is +3.6 points (95% CI [0.3, 7.1]); query removal yields substantive communication interactions of +9.5 points without additions and +8.5 with them. Participant-word-count interactions are +4.3 and −6.3 words per response, so substantive gains do not require consistently longer responses.Source: Table 40 · p. 69, §E.7.2 · p. 70
• A transcript audit attributed 44 of 47 selected Coordinator-selected-speaker failures to queries limiting response scope, but these selected cases are not population mechanism frequencies.In one selected episode, adding public PIU category labels and an instruction coincided with all five PIUs being communicated and all three final decisions succeeding, versus two PIUs and no successes without them.Source: §E.7.2 · p. 70
• The fixed-selection interventions identify effects of query content on communication and episode success, not effects of richer participant descriptions on coordinator selection or initial query generation.The design does not separate the labels-and-instruction effects on the selected participant from effects on later transcript readers, nor establish complete causal mediation or generalization to adaptive coordinators or the cross-domain regression.Source: §E.7.2 · p. 71

E.7.3. SARA: Source-Material and Transcript Interventions

• In SARA, source-material access is varied independently for participants assigned PIUs and those assigned none, while exact PIUs, descriptions, models, repetitions, and speaker order remain fixed.The four conditions provide no added source material, source material for PIU-assigned participants only, for no-PIU participants only, or for both groups; the experiment covers three communication structures and 2,376 primary episodes over 44 instances.Source: §E.7.3 · p. 72
• The transcript intervention holds participant messages and speaker order fixed, then regenerates the final decision from either the complete transcript or messages from the two PIU-assigned participants only.It uses frozen trajectories with no added source material or source material only for no-PIU participants, totaling 1,584 primary episodes over 44 instances; bootstrap intervals preserve matched conditions.Source: §E.7.3 · p. 72

E.7.4. SARA: Results and Scope

• The Simultaneous-responses versus Coordinator-selected-speaker interaction changed by −15.7 points with added source material, but the added-source estimate alone did not establish an ordering reversal.The added-source interaction estimate was −5.1 points (95% CI [−13.6, 3.0]).Source: §E.7.4 · p. 73, Table 42 · p. 73
• The interaction was not accompanied by a corresponding reduction in semantic completeness of communicated PIUs, motivating a test of what reaches the final decision maker.Under Simultaneous responses, no-PIU participants’ pooled message volume rose from approximately 371 to 1,396 tokens with source material, while PIU-assigned participants’ volume stayed near 204 tokens.Source: §E.7.4 · pp. 73–74
• Under Simultaneous responses, source material for participants assigned no PIU reduced episode success by 47.2 points, versus 14.9 points when supplied only to PIU-assigned participants.Once participants assigned no PIU had source material, adding it for PIU-assigned participants changed success by +0.8 points.Source: §E.7.4 · p. 74, Table 43 · p. 74
• Removing messages from participants assigned no PIU improved episode success by 47.7 points when they had source material, versus −1.0 points without it.The interaction was +48.7 points; replay results were similar across conditions, and the positive interaction appeared for all three reported models.Source: §E.7.4 · p. 74, Table 44 · p. 74
• The transcript intervention concerns source material given only to participants assigned no PIU and does not establish the same removal effect in other settings or communication structures.It also does not separate transcript length, distracting content, contradictory reasoning, and the final model’s attention allocation.Source: §E.7.4 · p. 75

E.8. Legal Token-Budget Ablations: Complete Results and Diagnostics

• Section 4.5 summarizes the principal findings and defers the complete legal token-budget analyses, diagnostics, and model- and corpus-level results to this appendix.The supplied passage introduces the deferred results presentation but does not report its findings.Source: §E.8 · p. 75

E.8.1. Complete Results Deferred from Section 4.5

• 55.3% to 78.6%: GPT-5.5 episode success rose as message budgets increased from 32 to 128 tokens, with no further improvement at 256 tokens.Variation across private-note budgets was smaller than variation across message budgets.Source: §E.8.1 · p. 76, Table 45 · p. 76

E.8.3. Local-Transcript Token Budgets

• Local-transcript budgets showed no monotonic success relationship: FIFO stayed within 6.9 points of unlimited, while random reading at 16 tokens averaged 10.3 points lower.At 16 tokens the coordinator query consumed the full budget, so FIFO and random reading exposed the same prefix; the 256-token condition reached 86.2% under FIFO and 82.8 ± 6.9% under random reading.Source: §E.8.1 · p. 76, Figure 12 · p. 76, §E.8.3 · pp. 77–78

E.8.2. Private-Note and Message Token Budgets

• GPT-5.5 message and private-note limits bound as intended, but Qwen3-32B showed no consistent relationship between either budget and success rate.GPT-5.5 messages were truncated in approximately 93%, 57%, 23%, and less than 1% of episodes as the message budget increased; private-note truncation fell from 82% to 4%.Source: §E.8.2 · p. 76, Table 46 · p. 77

E.9.1. Dependency Case and Episode Trajectory: CVS 2022

• In the CVS example, Sonnet 4.5 solved the task in all conditions, while Haiku 4.5 failed in both multi-agent conditions through communication or retrieval and fact-mapping failures.Both models solved it in Single-Agent All-PIU; no participant could calculate a ratio alone, and the final comparison required all four PIUs.Source: §E.9.1 · p. 79

E.9.2. Composite-Problem Episode Trajectory: Kirkland’s 2023

• Sonnet 4.5 recovered all six Kirkland PIUs, checked cross-passage support, and produced a fully correct, grounded six-component decision after 15 participant responses.The defensible synthesis linked additional financing to executing a turnaround under cash pressure, without claiming a specific loan funded a particular operating improvement.Source: §E.9.2 · pp. 80–81

F. Literature Motivation for the PIU-Distribution–Communication-Structure Interaction

• The literature motivates jointly examining PIU distribution and communication structure because communication must elicit and preserve the facts needed for a correct decision.The empirical specification includes their main effects and interaction, with a Bernoulli logit model, problem-family and model fixed effects, and standard errors clustered by problem instance; estimates are not causal tests of a theory.Source: F. Literature Motivation for the… · pp. 81–82

G. Policy-Training Data, Evaluation, and Diagnostic Analyses

• The two policy-training demonstrations compare policy collections and enforce explicit observation and communication budgets; only Coordinator-selected speaker requires participants to derive messages from source material.Current-speaker selection provides PIUs directly.Source: G. Policy-Training Data, Evaluation,… · p. 82

G.1.1. Construction and Data Splits

• GPT-5.5 generated and checked free-form legal questions, decisions, answer components, contradictions, and criteria while preserving PIU distributions; 283 of 396 instances passed on the first draft.The checks rejected reference-decision leakage, unsupported content, incomplete PIU coverage, and questions answerable from one PIU; remaining proposals required up to seven revision rounds.Source: §G.1.1 · p. 82, Table 48 · p. 83
• Across 396 instances, pivotal information counts have median 2, mean 2.13, and range 2–6; all 62 reference decisions score 1.0.The 62 CUAD-derived validation and MAUD-derived evaluation instances average six answer components; single-PIU partial decisions and original incorrect alternatives average 0.193. Policies never observe reference decisions, annotations, PIU identifiers, construction checks, or evaluation criteria.Source: §G.1.1 · p. 83

G.1.2. GPT-5.5 Evaluator

• GPT-5.5 assigns scores from 0 to 1, and their arithmetic mean across instances is the sole semantic training reward.Evaluation checks reference-conclusion agreement, required content, applicable numeric and legal conditions, and disqualifying errors; malformed, missing, or unavailable judge responses score zero. Evaluations use AWS Bedrock-hosted GPT-5.5 at temperature zero with a fixed prompt and normalization.Source: §G.1.2 · p. 83

G.2. Coordinator-selected speaker: Participant and Coordinator Policy Training

• In coordinator-selected-speaker episodes, participant policies send bounded messages from local observations, while a coordinator policy generates queries and the final decision.Each local observation has a 28,000-token budget; participant messages, coordinator queries, and final decisions have budgets of 48, 64, and 256 tokens, respectively; participants generate no private notes.Source: §G.2 · p. 83

G.2.1. Optimization and Training Configurations

• Training uses GRPO with eight CUAD-derived problems and eight rollouts per problem per update, for 80 updates; the LLM-judged score is the reward.Training updates all parameters with AdamW for one epoch per update using a PPO-style clipped surrogate; validation is every 10 updates with greedy decoding. Queried participants, query order, communicated PIUs, and whether every participant is queried do not affect reward.Source: §G.2.1 · p. 84

G.2.2. Two-Stage Policy Training

• Participant-only training changed messages and PIU coverage, leading a fixed coordinator to query a different participant in the insurance-obligations example.Table 51’s examples are illustrative, not frequency estimates, and do not enter training or checkpoint selection.Source: §G.2.2 · p. 84, Table 51 · p. 85
• With the trained participant policy held fixed, coordinator continuation changed queries in one example and yielded a correct final decision from substantively unchanged messages in another.Table 52’s examples are illustrative, not frequency estimates, and do not enter training or checkpoint selection.Source: §G.2.2 · p. 84, Table 52 · p. 85
• The examples distinguish changes arising from participant messages from those arising through coordinator queries or the final decision.The participant-only stage selected the update-60 checkpoint, while the coordinator-only continuation selected update 80.Source: §G.2.2 · pp. 84–85
• On 26 held-out MAUD-derived problem instances, two-stage policy training did not improve the aggregate LLM-judged score.The held-out instances were excluded from training and checkpoint selection.Source: §G.2.2 · p. 85

G.2.3. Joint Two-Policy Training

• The jointly trained policies’ mean LLM-judged score rises from 11.97% to 22.38% at update 80 on CUAD-derived validation evaluations.The update-80 pair has the highest mean score among scheduled evaluations; the coordinator queries every participant on all validation instances from update 20 through update 80.Source: §G.2.3 · p. 86
• On MAUD-derived instances, trained policies query and message every participant on all 26 problems, versus 20 of 26 under base policies, while scores change from 5.12% to 5.58%.In a CUAD-derived example, coordinated policies elicit both grant directions and score 62.5%, versus 12.5% for base policies, though the trained decision remains incomplete.Source: §G.2.3 · p. 86

G.3.1. Problem Instances and Communication Structure

• Training and held-out splits use FinDVer and FinLongDocQA instances; each participant initially receives one PIU, while shared observations provide the objective, format, and participant descriptions.The prompt checks cover 638 normalized instances and 4,988 rendered prompts, confirming that participants do not receive another participant’s PIU.Source: §G.3.1 · p. 86

G.3.2. Optimization and Checkpoint Selection

• A shared Qwen2.5-7B-Instruct participant policy is optimized with GRPO, and update 70 is selected using FinDVer validation scores.The 39 FinDVer validation instances determine checkpoint selection; the 21 FinLongDocQA validation instances do not.Source: §G.3.2 · p. 87

G.3.3. Communication Diagnostics

• Communication diagnostics measure final-decision completion, whether every participant sends a message, speaker coverage, unique speakers, and self-handoffs; none contributes to training reward.Diagnostics use one greedy rollout per problem instance and retain valid public actions produced before episode failure.Source: §G.3.3 · p. 87

G.3.4. Separating the Communication Trajectory from the Final-Decision Policy

• On validation, the communication-trajectory effect is 6.95 points (95% interval [0.49, 13.78]), while the final-decision-policy effect is −0.20 points (95% interval [−0.99, 0.61]).The paired cross-replay freezes the transcript, final decision maker, and final-decision prompt; one example scores 35% on the base trajectory and 100% on the trained trajectory under either final-decision policy.Source: §G.3.4 · pp. 87–88

G.3.5. Additional Analysis of the Communication Trajectories

• Table 53 reports paired trained-minus-base changes: FinDVer scores rise 12.62 points, while FinLongDocQA test scores fall 4.78 points.FinDVer also shows increases of 15.9 points in PIUs appearing in transcripts and 9.5 points in fully supported answer components; exact repetition rises 31.9 points on FinDVer and 25.5 on FinLongDocQA test.Source: Table 53 · p. 88, §G.3.5 · p. 89