# Prospective Experiment 4 protocol: human–AI economic coordination

**Freeze date:** 2026-10-31. **Status:** locally documented protocol, NOT deposited in an independent preregistration registry. Historical results from Experiments 1–3 have already been seen; hypotheses are informed by those pilots. All claims of confirmation must use *unseen seeds*, not development/pilot seeds. Do not alter this file after registration; amendments must be appended to a new file and compared to this version.

## Experimental units and estimands

Unit = independent exogenous economic path (seed). Arms receive matched shocks, types and private-signal draws (common random numbers); no post-treatment outcome can enter a decision. Primary outcome = average realized utilitarian surplus relative to a common ex-post, fully informed and instant-flexible capital upper bound, from periods `burn` through `T` (percentage regret, smaller is better). This benchmark is *infeasible* and must not be called an attainable planner. Secondary outcomes = preference-weighted principal utility, strategic regret under misreports, audit false-positive rate, output/price divergence, discovery delay, capital sorting Spearman rho, capital destroyed, collusion markup/HHI, computation cost and token/monetary costs of LLM calls. Report paired differences + bootstrap 95% CI across seeds; use Holm step-down family-wise 0.05 for H1–H7. Disclose non-significant, null and adverse results.

## Seven directional hypotheses (holdout only)

- **H1, information dispersion:** under positive report latency/noise, decentralized RL market has lower normalized regret than report-dependent central planner. Contrast MKT-RL minus PLAN-RL at L>=2, sigma>=0.1; expected negative.
- **H2, market manipulation:** collusion-capable market raises average producer markup and reduces net surplus relative to matched competitive market. Contrast COLL-RL minus MKT-RL; expected markup positive, surplus negative.
- **H3, constitutional restraint:** independent random audits plus proportional stake slashing reduce collusion losses without audit resource costs exceeding restored surplus. Contrast CONST-RL minus COLL-RL; expected net surplus positive and misbehavior negative.
- **H4, incentive compatibility:** a welfare/regret-trained Hybrid C allocation/payment rule yields lower *measured ex-post unilateral deviation gain* than a simple zero-transfer, report-proportional rule on unseen type profiles. Compare expected deviation regret; this is approximate IC, not proof of dominant strategy.
- **H5, endogenous gaming:** allowing agents to adapt their reports to planner payments/audits increases reporting distortion versus fixed honest reporting when audit intensity is zero; permitted direction is positive. Audit learning is separately hypothesized to reduce distortion relative to no-audit.
- **H6, principal–agent drift:** increasing brief-to-proxy drift lowers true principal utility even if proxy-performance is stable; periodic rebriefing reduces this gap. Compare drift=0.12 to 0 at matched shocks, and rebrief=5 to none.
- **H7, capital/discovery:** rising specificity and gestation increase capital misallocation and worsen recovery after a newly valuable good becomes discoverable; decentralized experimentation *may* lower discovery delay relative to the planner (exploratory, non-directional subtest, not part of family-wise H7).

## Frozen factors

Main factorial experiment (holdout, adaptive agents): regime `{MKT-RL, PLAN-RL, HYB-C, COLL-RL, CONST-RL}`, reporting `(L,sigma)={(0,0), (2,0.15)}`, human delegation drift `{0,0.12}`, audit regime `{none, adaptive}`, discovery `{off,on}`, `specificity zeta` `{0,0.5}`, `gestation` `{0,2}`. Some regimes make a factor inert; the driver flags and skips structurally redundant cells. Cost and evaluation feasibility determines explicit stop criteria, NOT outcome direction. Secondary stress grid fixes other factors at high friction and varies zeta `{0,0.1,0.5,0.85}` by gestation `{0,2,4}`. The intended full grid is specified in `config/experiment4_prereg.json` and generated from a deterministic manifest.

Capital, preference shock, producer productivity and private-signal innovations are coupled by seed across arms. Entrants discover previously hidden demand after a pre-announced technology/need arrival time, through private exploration signals; no current/future true demand data may leak into the report stream before reveal. Discovery opportunity is identical across arms, but actions determine discovery time.

## Pre-specification of learning and leakage controls

Tabular RL epsilon-greedy pricing/withholding actions and report factors trained online, with stable exploration schedule fixed independently of treatment outcome. For LLM tests, vendor/model ids, prompt hashes, temperatures, call budget, parse errors, retries, latency and token counts are disclosed; no fallback may silently reclassify RL as a vendor LLM. Hybrid C uses learned allocation *and payments* with truthful-utility welfare objective and sampled best-deviation regret penalties; training profiles must not overlap evaluation profiles. All reported incentive-regret bounds are empirical over a discretized misreport grid; do not assert exact strategyproofness. Human principals may be synthetic briefs only in the pilot, and genuine briefs require separate human participant input and explicit consent. Transaction calibration requires real anonymized transaction records and, for drift, paired independent principal-utility elicitation; payment volumes alone cannot identify preferences.

**Development / pilot seeds:** 1–50 only. **Locked confirmatory seeds:** 1001–1200 (200 independent units; planned sample size, subject to documented feasibility constraints). **Train-only mechanism seeds:** 40001–49999. **Validation-only mechanism seeds:** 50001–50999. Excluded seeds and incomplete LLM calls must be reported. No trial can use future true valuations, future shock realizations or ex-post benchmark when making decisions. Outcomes are generated by physical allocations, utilities and costs, not regime labels.

## Analysis and limitations

The main H1/H2/H3/H5/H6/H7 estimands are paired mean contrasts over seed, using common paths and identical random action noise streams. H4 uses a disjoint held-out type profile set. Report both intent-to-treat (including agents with parse errors/timeouts) and per-protocol results. Cache mechanisms trained on training profiles and freeze weights before holdout outcomes. Pre-register time horizons T=40, burn=8, n_principals=12, n_producers=3, n_goods=3 for a computational pilot; holdout should re-evaluate with N=32/J=5/T=80 (scaling sensitivity). Meaningful real-world inference requires richer cost technology, actual stakeholders, external calibration, dynamic entry and policy safeguards. Code-level plausibility and falsifiability, not field causation, are the near-term goal.