\section{Results}
\begin{figure}[ht]
    \centering
    \input{chapters/figures/supra/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}

Distinguishability 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 full recorded cohort contains 13 human sessions and 16 agent sessions, and the table below reports the corresponding group-level statistics and 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 & 13 & $-3.35$ & $2.67$ \\
Agent sessions & 16 & $+1.65$ & $2.83$ \\
\midrule
\multicolumn{4}{l}{Mann-Whitney two-sided test: $p<0.001$} \\
\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 test result (p less than 0.001) at n=13 humans and n=16 agents indicates strong rank distinction between groups, providing evidence that the transition kernels are distinguishable 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) a baseline policy with revenue-only reward.

\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} \\
Baseline policy & \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 (p less than 0.001) confirms that per-session divergence gaps distinguish the two actor classes with near-zero overlap in rank ordering. This is the condition required for distinguishability to act as a useful control signal in the pricing loop rather than just an auxiliary classifier score.

\subsection{Anomalies}
