\section{Limitations}
\label{sec:limitations}

The results of this paper are causal statements about a simulator. Every limitation below bounds
what they can say about actual markets, and several bound what they can say about the simulator itself.

\paragraph{Internal validity.}
The confirmatory design uses seven matched seeds per live cell. With paired inference this gives
80\,\% power only for standardized effects of roughly $d \approx 1.2$ (Section~\ref{sec:identification});
smaller effects are reported with their confidence intervals and must be read as inconclusive rather
than absent. The seed count was fixed by the monetary cap on API calls (about 40~USD for the whole
project), not by a pilot variance estimate, and the pilot ran concurrently with the confirmatory
design on the same frozen code revision; the pilot therefore informs cost, validity and realized-dose
reporting but did not feed back into the design. The thresholds that define bubbles and crashes were
pre-registered, and the control economy exhibits a floor effect at the crash threshold (no crashes in
30 control seeds), so crash frequencies can only increase under treatment; the sensitivity grid in
Section~\ref{sec:robustness} reports how the conclusions move with the thresholds.

\paragraph{Provider coverage.}
All live cells use one provider family (OpenAI, \code{gpt-5.4-nano} as the primary model and
\code{gpt-5.4-mini} in the two-model and equal-budget arms). The Anthropic adapter is implemented and
exercised with the mock provider, but the key available when the experiments were run was rejected by
the API, so no Claude-populated market is reported. The cross-provider comparison that the research
questions call for is therefore reduced to a within-provider comparison of two model sizes, and the
``shared-model'' mechanism is tested through prompt diversity and the model mix rather than through
genuinely different foundation-model families. The two-model arm is compared with the single-model
diverse-prompt arm only; the mini-only cell needed to decompose a model-mix effect into a composition
effect and a diversity effect was not run.

\paragraph{What the LLM agents are.}
An LLM agent here is a small reasoning model answering a short, fixed prompt every twenty ticks with a
strictly validated JSON action. It has no tools, no retrieval, no fine-tuning and, outside the memory
and channel arms, no state. The rationale field is logged but is never treated as evidence about the
model's internal reasoning. Decision frequency is deliberately separated from event frequency: an LLM
agent makes 27~decisions in a 600-tick run while classical agents act on roughly one tick in five, so
the realized share of orders and volume is far below the assigned share of trader slots; both are
reported and the dose--response is read on the assigned share only. Provider outputs are not
deterministic across repeated calls; recorded decisions are cached and replayed exactly, and cache hits
are counted separately from online calls. The frozen nearest-neighbour library used to scale the
population to 1,000 traders is a non-adaptive approximation of recorded behaviour and is reported as a
separate arm, never pooled with online runs.

\paragraph{The economy.}
The exchange is a partial-equilibrium sandbox: dividends, discount rate, endowments and noise trading
are exogenous; there is no entry, no learning across runs, no short selling by default, and the
market makers follow a bounded inventory rule rather than an optimizing strategy. The stylized model of
Section~\ref{sec:theory} shares these restrictions: linear order submission, a competitive risk-neutral
market maker, Gaussian primitives and a fixed pricing schedule in the feedback extension. Its
propositions are statements about that model; the simulator tests their comparative statics, not their
closed forms. The classical population was calibrated to reproduce a short list of stylized facts
(near-zero return autocorrelation, fat tails, volatility clustering, spreads of 10--30 basis points) at
$N = 100$, and the same activity rates produce a somewhat different microstructure at $N = 1{,}000$ and
$N = 10{,}000$ unless the activity rate is scaled; all penetration experiments are run at $N = 100$.

\paragraph{External validity.}
Simulated LLM traders are not institutions, and the market here has no regulation, no intermediaries
beyond five quoting agents, no overnight, and no cross-market linkages beyond the two-asset arm. Nothing
in the paper should be read as evidence about how deployed trading systems behave. The claim is narrower:
within a transparent, replayable economy, raising the share of traders driven by one language model
changes price discovery and coordination in the direction, and through the channel, that a
correlated-error model predicts, and those changes can be undone or amplified by interventions that
real markets can also implement. Whether the same mechanism operates at scale in live markets is an
empirical question this design cannot answer.