\section{Results}
\begin{figure}[ht]
    \centering
    \input{chapters/figures/supra.tex}
    \caption{Evolution of price distributions over experiment steps. The heatmap illustrates the density of price offerings. This is an early baseline simulation which demonstrates supra-competitive price-setting in deep learning agents such as SAC as can be clearly seen by the high density at the highest available price.}
    \label{fig:supra_heatmap}
\end{figure}

\subsection{Behavioral Analysis}

Separability between human and agent sessions is evaluated by computing per-session divergence gap scores (how much closer each session is to the human baseline versus the agent baseline) and comparing the two groups with a Mann-Whitney U test. The table below reports the group-level descriptive statistics for the gap scores and the test result.

\begin{table}[ht]
\centering
\caption{Per-session divergence gap (distance to human baseline minus distance to agent baseline) by actor class with Mann-Whitney U test.}
\label{tab:divergence_significance}
\begin{tabular}{lccc}
\toprule
Group & n & Mean gap & Std \\
\midrule
Human sessions & 11 & $-3.3522$ & $2.6748$ \\
Agent sessions & 6 & $+1.6482$ & $2.8349$ \\
\midrule
\multicolumn{4}{l}{Mann-Whitney $U = 2.0$, $p = 0.0006$ (two-sided)} \\
\bottomrule
\end{tabular}
\end{table}

The sign structure is consistent with the theoretical expectation: human sessions produce negative gap scores (closer to the human centroid, far from the agent centroid) while agent sessions produce positive gap scores (closer to the agent centroid). The two-sided p-value of 0.0006 (which means there is only a 0.06\% chance this pattern occurred by random luck) indicates near-complete rank separation between the groups at n=11 humans and n=6 agents, providing strong evidence that the transition kernels are separable enough to justify their use as a control signal in downstream pricing.

\subsection{Experimental Outcomes}

To evaluate robustness contributions, we compare two policies on the same environment family: (i) robust pricing with COI-aware reward and adversarial contamination step, and (ii) non-robust baseline with revenue-only reward (no-robust flag).

\begin{table}[ht]
\centering
\caption{Pricing policy benchmark for robust vs non-robust training.}
\label{tab:pricing_benchmark}
\begin{tabular}{lcccc}
\toprule
Policy & Eval reward & Eval revenue & COI leakage & Margin collapse rate \\
\midrule
Robust policy & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
Non-robust baseline (\texttt{--no-robust}) & \textit{TBD} & \textit{TBD} & \textit{TBD} & \textit{TBD} \\
\bottomrule
\end{tabular}
\end{table}

This comparison isolates the effect of robustness terms from model capacity and optimization settings, and provides the benchmark needed for interpreting the value of COI-aware control.

\subsection{Interpretation and Insights}

The Mann-Whitney result (U=2.0, p less than 0.001) confirms that per-session divergence gaps separate the two actor classes with near-zero overlap in rank ordering. This is the condition required for separability to act as a useful control signal in the pricing loop rather than just an auxiliary classifier score.

\subsection{Anomalies}
