Team Theory Foundations

10 canonical team-theory primitives for cooperative multi-agent decision problems — agents share a payoff but each sees a different slice of the world. Game theory handles strategic conflict; decision theory handles solo choice under uncertainty; team theory handles the regime in between, which is exactly where subagents and orchestrated AI agents operate.

The field was founded by Jacob Marschak (1955) and formalized by Roy Radner (1962). It is the formal basis for: when to centralize a decision, what each agent must observe, when communication pays for itself, and why decentralized teams can be optimal even with free communication channels. Modern multi-agent reinforcement learning (Dec-POMDPs, MARL) is its computational descendant.

When to Apply

Apply team-theory when:

• Multiple agents with shared payoff but partitioned observations (the canonical subagent setting)
• Designing what each subagent sees vs. what is centralized
• Choosing between centralized orchestrator, decentralized swarm, and hierarchical structures
• Costing communication: is it worth the latency / token / coordination overhead?
• Building agent teams where role specialization matters (each agent owns a different observation lane)
• Multi-agent RL or Dec-POMDP problem framing

Skip and use simpler alternatives when:

• Agents have divergent incentives → use foundations-game-theory (mechanism design, auctions, debates)
• Single agent / single-shot decision under uncertainty → use foundations-decision-theory
• Communication itself is the bottleneck on a known structure → use foundations-information-theory (channel capacity)
• The problem is recursive control of a viable system, not a one-shot team decision → use foundations-cybernetics-vsm
• All agents see the same information — information partitioning offers no advantage by itself; compare a single decision-maker baseline while accounting for distinct capabilities and constraints

Contents

• Quick Reference
• Primitive Index
• Formal Supporting Theory
• Anti-Patterns
• Decision Checklist
• Composition Recipes
• Workflow
• ASCII Flow
• Navigation
• Related Skills
• Fact-Checking

Quick Reference

Full definitions, inputs, outputs, failure modes, and worked examples: references/primitives-overview.md.

Primitive Index

Formal Supporting Theory

See references/primitives-overview.md for the formal-theory map and theorem statements.

Anti-Patterns

Decision Checklist

• Shared payoff? If no, exit to foundations-game-theory. If yes, continue (#10)
• What does each agent observe? Map the information structure explicitly (#2)
• Are observations redundant? Trim — observation has cost (#7)
• Is communication channel justified? Compute expected payoff lift; reject if < cost (#4)
• Is the communication topology justified by actual dependencies and a matched-budget local comparison? Moderate sparsity is a tested candidate, not a universal requirement.
• Does the team meet the precise Gaussian/quadratic, convexity and information-structure assumptions? Approximate resemblance alone does not license Radner’s linear-policy result (#5)
• Does an action affect later observations, and what information is nested? Classify the information sets before invoking non-classical results; action dependence alone is insufficient (#6)
• Sequential decisions over time with state? Frame as Dec-POMDP (#9)
• Picked an organizational form? Centralized / decentralized / hierarchical — justify choice against the alternatives (#8)
• Tested joint alternatives, not just person-by-person tuning? Vary joint policies; finite comparisons do not certify a global optimum (#3)
• Does the aggregation rule weight by competence, or does it pool? If agents differ in task-relevant skill, opinion pooling destroys the expert's advantage; route or weight instead (#3, Pappu et al. 2026). Check the single-best-member baseline before shipping any team design
• Human virtual/distributed team? Consider task and medium evidence alongside accessibility, latency and participant constraints; no universal video-first rule follows. Human media findings do not establish LLM transport choices.

Composition Recipes

Designing a subagent team for a research task

Context: Orchestrator needs to dispatch N subagents on a multi-source research task with a shared answer goal.

1. Verify common-task condition (#10): all subagents and orchestrator share the payoff "produce one accurate answer." If not, exit to game-theory.
2. Map information structure (#2): which sources/files/tools does each subagent observe? Avoid redundant assignment. For human-in-the-loop teams: the temporal ordering of observation matters — simultaneous presentation of human and AI outputs outperforms sequential (human-first then AI) on average (npj Artificial Intelligence 2025, N=52 clinical studies). Design observation lanes with this moderator in mind. CTP conditions (Hemmer et al. 2024, EJIS 2025): human-AI complementarity — performance exceeding either agent or human alone — requires either (a) information asymmetry (human has local context AI lacks) or (b) capability asymmetry (human provides judgment on novel cases AI cannot handle). These are candidate performance-complementarity conditions, not permission to remove oversight: human participation may be required for authority, rights, accountability or safety even without an accuracy gain. Test local performance and preserve those duties.
3. Cost observations (#7): each tool call has token + latency cost. Compare the joint value and cost of observation bundles. Diminishing marginal value requires assumptions; complementary observations can have increasing value.
4. Compute value of communication (#4): does mid-task chatter between subagents lift expected payoff more than its cost? Test communication when observations, constraints or intermediate decisions interact; late synthesis is a candidate for low coupling, not a theorem-backed default.
5. Pick organizational form (#8): compare single-agent, split-and-merge, centralized and hierarchical candidates at matched total budgets. Use split-and-merge for separable work only when aggregation and shared constraints remain adequate; LQG analogy supplies no default.
6. Compare bounded joint-policy candidates (#3). An improving pairwise deviation disproves team optimality but does not establish prior person-by-person optimality; report the best tested candidate and uncertainty, with no global certificate.

Choosing between orchestrator-led and swarm forms

Context: A product team must pick between a single planner agent that delegates everything (centralized) and a peer-to-peer agent network (decentralized).

1. Invoke #5 only for an explicitly modeled problem satisfying the exact quadratic, Gaussian, convexity and information-structure premises of the applicable theorem. Similarity to LQG gives no upper bound for LLM architectures; otherwise compare matched-budget candidates.
2. Cost the communication channel: orchestrator-led requires every observation to flow up and every decision to flow down. Decentralized requires only local observation but needs convergence on the synthesis.
3. Apply #8: high information cost and low coupling motivate a decentralized candidate; low information cost and high coupling motivate a centralized candidate. Compare them locally; these heuristics do not prove dominance. For parallelizable subtasks where feasible, add a fourth candidate: emergent self-organization with minimal structure (sequential protocol + autonomous role assignment). Reported scaling results are architecture-, benchmark- and budget-dependent; do not infer a universal four-agent threshold or hierarchy disadvantage. Justified by Dochkina (2026, arXiv:2603.28990) and CARD (Wu et al., ICLR 2026).
4. Worked example: code review across 5 files. Files are independent (no signaling, low coupling). A decentralized candidate (5 parallel reviewers + final aggregator) may reduce duplicated observations; compare total cost and verification quality against an orchestrator-led baseline. Code review across one tightly-coupled module: signaling is high (one agent's finding changes another's interpretation); test centralized or hierarchical coordination rather than assuming a winner.

Sizing the orchestrator's context budget

Context: How much should the orchestrator observe vs. push down to subagents?

1. Apply #7: every token in the orchestrator's context has cost. Give the orchestrator the information needed for assignment, synthesis and verification, including domain evidence when its conclusions depend on that evidence.
2. Apply #2: start with task graph, roster and status, then add decision-relevant object-level evidence and provenance needed to check worker claims.
3. Anti-pattern: orchestrator reads all source files and then asks subagents to summarize them — observation paid for twice. Fix: delegate first-pass source reading, then return claims with source locations, assumptions and counterevidence; the orchestrator reads underlying contents where synthesis or verification needs them.

Designing subagent context as an information-structure problem (AI app builders)

Context: You are building a multi-agent AI application and must decide what context (system prompt, retrieved docs, tool permissions, conversation history) each subagent receives.

1. Name the information structure first (#2). For each subagent, write a one-row entry: agent | observation sources | action produced. This is the η partition — make it explicit before writing any code.
2. Apply the task-type rule. For separable subtasks, consider partitioned observations with shared goal, acceptance criteria, constraints and necessary interfaces. For coupled subtasks, compare centralized, hierarchical or communicating candidates; pass decision outputs with evidence, uncertainty and provenance needed downstream. A raw reasoning trace is not required, but verified source evidence may be.
3. Strip context to decision-relevant signals (#7). Each token in a subagent's context window is an observation cost. Give the subagent only what changes its action. If a document section never alters the subagent's output, remove it from its context.
4. Check for signaling (#6). If A’s output affects B’s context, inspect whether B also knows A’s relevant information; output dependence alone does not establish non-classical territory. Do not assume A's optimal policy is the same as if it were working in isolation — A should write with B's downstream use in mind (nonlinear policy).
5. Compute value of communication before adding agent-to-agent messaging (#4). Does mid-task chatter between subagents increase the joint answer quality by more than the latency + token cost? Use task coupling and missing information to motivate communication candidates; compare costs and quality locally rather than imposing a blanket no-communication rule.
6. Compare decentralized + late synthesis with a central baseline at matched budgets. Count total observation, communication and synthesis costs; O(1) per-agent work does not imply O(1) total system cost. No universal four-agent threshold is established.

Workflow

1. Confirm common-task condition (#10). If payoffs diverge, exit to game-theory.
2. Map the information structure (#2): one agent per row, one observation source per column, fill the matrix.
3. Cost the observations (#7) and the communication channels (#4).
4. Pick organizational form (#8) — centralized, decentralized, hierarchical — justified against alternatives.
5. Verify the exact theorem premises before applying a linear-policy result (#5). Inspect information nestedness when actions affect observations (#6); dependence alone does not disqualify partially nested cases. Otherwise evaluate bounded policy candidates.
6. Report best tested joint policy (#3), searched deviations and uncertainty. Do not certify global optimality from unilateral or pairwise search.
7. For sequential problems with state, frame as Dec-POMDP (#9) and pick an MARL solver.

ASCII Flow

Cooperative multi-agent decision
  -> Confirm shared payoff and common-task condition
     +-- payoff diverges -> exit to game theory
     +-- shared payoff holds -> map information structure
  -> Cost observation and communication channels
  -> Choose centralized, decentralized, or hierarchical form
  -> Compare bounded joint policies and sequential-state needs
  -> Return team design, information lanes, communication rule, and solver path

Local Validation Artifact

• Operational record, worked case and regression checks. Read before translating a mechanism into a deployment recommendation.

Navigation

• Domain-agnostic primitives overview: references/primitives-overview.md
• Formal theory map and production boundaries: references/formal-theory-map.md
• Patterns, scenarios, and traps for multi-agent / subagent design: references/patterns-scenarios-traps.md
• Measuring the information structure you actually have — Westrum typology and the seven validated culture survey items (Accelerate, 2018): references/westrum-culture-measurement.md
• Sources: data/sources.json

Related Skills

• foundations-game-theory — exit here when payoffs diverge
• foundations-decision-theory — single-agent uncertain choice
• foundations-information-theory — pricing the channel
• foundations-cybernetics-vsm — recursive viable-system control
• foundations-grounding-communication — how agents share state once you decide they should (see also: temporal information structure in human-AI teams — primitive #2, npj AI 2025)
• agents-subagents — applied subagent patterns
• agents-swarm-orchestration — applied multi-agent orchestration

Fact-Checking

• Marschak (1955) "Elements for a Theory of Teams." Management Science 1(2). Founded the field.
• Marschak and Radner (1972) Economic Theory of Teams. Yale. Canonical text.
• Radner (1962) "Team Decision Problems." Annals of Mathematical Statistics 33(3). LQG theorem.
• Witsenhausen (1968) "A Counterexample in Stochastic Optimum Control." SIAM J. Control 6(1). Nonlinear-dominance result.
• Bernstein, Givan, Immerman, Zilberstein (2002) "The Complexity of Decentralized Control of Markov Decision Processes." Math. of Operations Research. Dec-POMDP framing — NEXP-complete.
• Oliehoek and Amato (2016) A Concise Introduction to Decentralized POMDPs. Springer.
• Numeric thresholds (cost-of-communication, observation budgets) are domain-specific. Verify against primary references before using as decision authority.
• Brooks, F.P. (1975/1995) The Mythical Man-Month. Addison-Wesley. Source for the team-size / coordination-cost curve (#8b): pairwise coordination links grow combinatorially with team size, used here as a qualitative mechanism, not a quantitative team-theory result.
• Eldor, Hodor, and Cappelli (2023) "The limits of psychological safety: Nonlinear relationships with performance." Organizational Behavior and Human Decision Processes 177, article 104255. Primary empirical source for the curvilinear boundary condition cited via Edmondson & Bransby (2023). Title, authors, volume, and article number confirmed 2026-08-14; full text remains paywalled. No independent replication located as of 2026-08-14, and the paper has drawn (non-peer-reviewed) methodological criticism over supervisor-rated performance measures and the arbitrariness of the 80–90th-percentile turning point — do not present the inverted-U as a settled effect.
• Collective-intelligence caveat: Rowe, Hattie, and Hester (2021) "g versus c: comparing individual and collective intelligence across two meta-analyses." Cognitive Research: Principles and Implications. Pooled 857 groups across nine criterion tasks; c-factor correlates r=.26 (95% CI .10–.40) with group performance, and all but four studies failed to control for members' individual intelligence. Rowe, Hattie, and Munro (2024, PLOS ONE 19, e0307945, N=85 individuals in 29 groups) favor a two-factor fluid/crystallized model over Woolley et al.'s (2010) single c-factor. Small samples on both sides — cite as "contested," not "refuted."
• Expertise aggregation failure: Pappu et al. (2026), "Multi-Agent Teams Hold Experts Back," arXiv:2602.01011. In Table 2 and §4.2, the 41.1% relative synergy gap is HLE Text-Only, Expert Not Mentioned: team accuracy 28.0% versus the At Least One Correct oracle bound 47.5%. It is not a 41.1% loss against the best fixed individual (29.0%); the Reveal Expert team scores 36.0%. Controlled psychology tasks separately show expertise dilution and team-size effects. Do not transfer the abstract's broad comparator wording into a benchmark claim.
• DPI argument for single-agent dominance: Tran & Kiela (2026, arXiv:2604.02460) demonstrate empirically across four model families and five MAS architectures that single-agent systems match or exceed multi-agent on multi-hop reasoning under equal token budgets, with theoretical grounding in the Data Processing Inequality.
• Latent-space inter-agent communication: LatentMAS (Zou et al. 2025, arXiv:2511.20639). Section 4.1 reports an average 14.6% accuracy improvement over the single-model baseline in its sequential setting; the reported sequential gain over text-based MAS is 2.8%, with 4× average inference speedup against sequential TextMAS. These are architecture- and benchmark-specific results, not a portable guarantee for arbitrary agents. Preserve the authors' units rather than converting to percentage points without table-level calculation.
• Emergent self-organization at scale: Dochkina (2026, arXiv:2603.28990, IEEE Access) demonstrates across 25,000 tasks and 8 model families that self-organizing agents with minimal structure outperform designed hierarchies by 14% (Cohen's d=1.86) and scale sub-linearly to 256 agents. Corroborated by CARD (Wu et al., ICLR 2026) and MegaAgent (ACL 2025).
• Human-AI teaming mode as information structure: Systematic review (npj AI, Nature portfolio, December 2025, N=52 clinical studies) finds simultaneous human-AI observation outperforms sequential mode; corroborated by PRISMA review of 104 studies (Kargarnovin et al., Frontiers in Robotics and AI, 2026) and PNAS Nexus complementarity framework (Gonzalez et al., 2026).

Learnings Loop

When prior decisions or pitfalls are relevant, consult learnings.consolidated.md if present; use learnings.md only for needed history or as the available fallback. Otherwise skip both.

After applying it, if you encountered a pattern worth remembering, a mistake worth preventing, or a domain fact that surprised you, append one dated bullet to learnings.md via agents-skills-feedback-loop/scripts/append_learning.py. Do not modify SKILL.md itself.