\section{Results III: agentic markets, herding, credit and the LLM laboratory}
\label{sec:results_c}

All results in this section are bounded-rationality simulated outcomes (Section~\ref{sec:markets}). The Bayesian
mean-variance control is reported first; LLM agents are read against it.

\subsection{Common-model herding (H2)}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figC_herding.pdf}
\caption{Model C, Bayesian control: average pairwise correlation of order flow across agents after residualising on
public information, by market design, delegation share and number of independent models (20 seeds, common random
numbers, bootstrap 95\% bands). Source: \texttt{scripts/30\_model\_c.py}.}
\label{fig:C_herding}
\end{figure}

Figure~\ref{fig:C_herding} and Table~\ref{tab:c_factorial} test H2 in its pre-registered form. In the Walrasian call
the order-flow correlation conditional on public information rises from \numofcwalrasianzero\ with private signals to
\numofcwalrasianoneone\ when everyone acts on one model, and falls to \numofcwalrasianonefour\ with four models and
\numofcwalrasianoneeight\ with eight; the bootstrap bands do not overlap. The within-delegator correlation is close
to one with a single model in the call market and declines with $M$ roughly as the theory's $1/M$ loading predicts
(the residual correlation at large $M$ is the common response to public dividends that the residualisation does not
fully remove). The continuous double auction and bilateral bargaining show the same pattern with lower levels
(\numofccdaoneone\ and 0.86 at $D=1$, $M=1$): sequential execution and random matching break up some of the
correlation that a call market preserves. H2's falsification condition is not met in any design.

\input{tables/model_c_factorial}

\subsection{Volume, volatility and the disagreement channel}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figC_volatility_volume.pdf}
\caption{Model C, continuous double auction, Bayesian control: (a) return volatility and (b) trades per period as a
function of the delegation share and the number of models. Source: \texttt{scripts/30\_model\_c.py}.}
\label{fig:C_volvol}
\end{figure}

The competing explanation anticipated in the novelty audit is visible in Figure~\ref{fig:C_volvol}: with one shared
model, trading volume falls from \numtradescdazero\ to \numtradescdaoneone\ trades per period in the double auction
(from \numtradeswalrasianzero\ to \numtradeswalrasianoneone\ in the call market, close to the no-trade theorem) and
unconditional volatility does not rise. Homogenisation removes the disagreement that generates trade. Under leverage
this has a benign side: with a borrowing cap of half of equity, defaults and forced sales are \emph{highest} with
private signals and fall as $D$ rises (Table~\ref{tab:c_factorial} notes; Figure~\ref{fig:C_designs}), because fewer
trades mean less leverage taken. The shared model makes the market quieter and more correlated at the same time.
Fragility therefore has to be looked for conditional on a shock, which is the point of the stress test.

\subsection{Collateral amplification under a false shared signal (H4, H5)}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figC_stress.pdf}
\caption{Stress test: all agents delegate, a $-10$ s.d.\ common model error arrives at mid-sample, dividends are
persistent ($\rho_d=0.95$) and the liquidity ladder is thin. (a) Cumulative return over the shock window
(bootstrap 95\% intervals, 20 seeds); (b) forced sales. ``Levered'' agents have borrowed 95\% of their margin
capacity before the shock. Source: \texttt{scripts/30\_model\_c.py}.}
\label{fig:C_stress}
\end{figure}

Table~\ref{tab:c_stress} and Figure~\ref{fig:C_stress} report the stress test. In the Walrasian call with a single
model, the false signal moves the price by \numstressRetWunlevOne\% over the shock window when agents are unlevered;
when agents start at 95\% of their margin capacity with a 20\% margin, forced sales of \numstressForcedWlevTwenty\
shares push the cumulative return to \numstressRetWlevTwenty\%, an amplification factor of \numstressAmp. A 50\%
margin (Regulation T) cuts the amplification to \numstressAmpFifty\ (return \numstressRetWlevFifty\%), which is H5's
leverage-limit prediction. With four independent models the same shock---applied to every model, so that only the
pre-shock heterogeneity differs---produces \numstressRetWlevTwentyMfour\% and no forced sales: the diversity of
models had already diluted the correlated positions that the spiral needs. A three-period persistent error deepens the
spiral (\numstressRetWlevTwentyPersist\%).

The double auction behaves differently. The price trough is similar (\numstressTroughCunlevOne\% unlevered,
\numstressTroughClevTwenty\% levered) but the cumulative return over the window is near zero and forced sales are
small: sequential execution against the ladder lets the price recover within the period once the sellers are done,
so the marked price at the next margin check is not low enough to trigger a cascade. H4 is therefore supported in the
call-market design, where one clearing price per period carries the full weight of correlated orders, and not in the
continuous design under our rules. We regard this design dependence as a substantive finding: whether model noise is
amplified by collateral depends on how execution translates correlated orders into a marked price, which is exactly
the distinction between equilibrium prices and execution prices that the pre-registration insisted on.

\input{tables/model_c_stress}

\subsection{LLM agents}

\input{tables/llm_lab}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figL_llm_lab.pdf}
\caption{LLM laboratory (CDA, temperature 0): (a) order-flow correlation conditional on public information and
(b) trades per period, by policy family and signal structure. Source: \texttt{scripts/35\_llm\_lab.py}.}
\label{fig:L_lab}
\end{figure}

Table~\ref{tab:llm} and Figure~\ref{fig:L_lab} report the live-inference cells (\numllmCalls\ calls,
\numllmTokens\ tokens, zero marginal cost on local hardware, \numllmInvalid\ invalid actions in total). Three
findings are robust across seeds and temperatures. First, the H2 pattern survives the change of policy family: with a
shared signal the conditional order-flow correlation of Qwen2.5-7B agents is \numllmsharedoneone, against
\numllmsharedzero\ with private signals, and three heterogeneous models with three signals give
\numllmdiverseonethree; the Bayesian control gives \numllmbayesoneone\ and \numllmbayeszero. Second, LLM agents trade
more than the Bayesian control under a shared signal (\numllmsharedoneonetrades\ versus \numllmbayesoneonetrades\
trades per period): they do not fully recognise that an identical signal leaves no gains from trade, so the no-trade
outcome of the control is replaced by churning at slightly dispersed limit prices. Third, model identity matters more
than prompt wording: five prompt variants on one model move the correlation less than switching models does, and
Mistral-7B and Llama-3.2-3B differ from Qwen both in validity rates (Mistral rejects a system role and returns
more schema-invalid actions; Llama holds more often) and in order aggressiveness. None of this is evidence about human
behaviour; it shows that the architecture---one model or several, hard constraints, structured observations---shapes
the correlation structure of an agentic market in the direction the theory predicts, and that the \emph{effective}
number of models is the relevant policy variable.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.6\textwidth]{figL_cost_frontier.pdf}
\caption{Inference cost frontier: wall-clock time per run against invalid actions per run, by policy family (local
4-bit inference on Apple-silicon nodes). Source: \texttt{scripts/35\_llm\_lab.py}.}
\label{fig:L_cost}
\end{figure}