PHANTOM/paper/src/main.tex

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\begin{titlepage}
    \centering
    \includegraphics[width=\textwidth]{graphics/banner.png}\\[0.8cm]
    \LARGE\textbf{PHANTOM: Pricing Heuristics Against Non-human Transaction Orchestration Mechanisms}\\[0.5cm]
    \Large\textbf{Daniel Rösel}\\
    \large\textit{Bachelor of Computer Science \& Artificial Intelligence}\\[0.5cm]
    \Large\textit{Supervised by:}\\
    \Large\textbf{Alberto Martín Izquierdo}\\
    \large\textit{IE University, Madrid, Spain}\\[1cm]
    \large\today
\end{titlepage}

\begin{abstract}
With accelerated growth of Lager Language Model agents in e-commerce a novel adversarial dynamic to digital markets emerges. This paper address the vulnerability of dynamic pricing systems to AI intermediaries that decouple the information gather stages from the transaction execution. By conducing reconnaissance isolates sessions, agents circumvent the ``Cost of Information'' (COI) defined as the accumulated price premium typically thought demand expression estimators.
We formally define this phenomenon and derive the Cost of Information Theorem, proving that as the saturation of independent, utility-maximizing agents increases, the platform’s ability to sustain a COI converges to zero, rendering standard dynamic pricing mechanisms incentive-incompatible.
To respond to this threat we propose a defensive framework which integrates behavioral economics with Adversarially Distributionally Robust Optimization (DRO). We introduce a custom e-commerce research platform built on hybrid Kappa-Lambda architecture, designed to capture and simulate high-fidelity controlled interaction trajectories. We further demonstrate through modeling that human and agent behaviors exhibit distinct transition probability kernels, enabling the construction of discriminative models based on Kullback-Leibler divergence.
These behavioral signals serve as inputs for a Distributionally Robust Reinforcement Learning (DR-RL) agent. We formulate the pricing problem as a Stackelberg game where the learner optimizes against an ambiguity set of demand distributions defined by the Wasserstein distance. This approach allows the pricing policy to remain robust against non-stationary contamination without overfitting to deterministic demand curves. The research validates a mechanism for preserving margin integrity and market equilibrium in an agent-mediated economy, while minimizing degradation to the legitimate human user experience (UX).
\end{abstract}

\noindent\textbf{Keywords:} Dynamic Pricing, LLM Agents, Adversarial Machine Learning, E-commerce, Behavioral Detection, Reinforcement Learning

\vspace{1em}
\noindent\textbf{Acknowledgments:} This research was supported by the TPU Research Cloud program, which provided access to Google Cloud TPU accelerators (including TPU v4, v5e, and v6e).

\vspace{0.5em}
\noindent\textbf{Project page:} \url{https://velocitatem.github.io/PHANTOM/}

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\input{chapters/01-intro}
\input{chapters/02-literature-review}
\input{chapters/03-methodology}
\input{chapters/04-results}
\input{chapters/05-discussion}
\input{chapters/06-conclusion}

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\appendix
\section{Terminology}
\begin{description}
\item[Agent $A$] A non-human actor, typically an LLM-driven system that executes web actions toward a goal.
\item[Human $H$] A human participant interacting with the platform to complete a task.
\item[Actor Type $\theta$] A latent class parameter describing whether a session is generated by a human or an agent profile.
\item[Platform] A web interface exposing purchasable items and their offered prices.
\item[Session $s$] A bounded interaction record tied to one actor and one session identifier.
\item[Event $e_{s,k}$] A single interaction tuple in a session, including action, item target, and timestamp.
\item[Trajectory $\tau_s$] The ordered sequence of events generated within a session.
\item[Demand Proxy $\hat{q}_{t,i}$] A weighted aggregate of observed actions used as an operational substitute for latent demand.
\item[Action Weight Function $\omega(a)$] A mapping from action type to signal strength in the demand proxy.
\item[True Demand $d(p;\theta)$] The latent purchase response as a function of price and actor type.
\item[Contamination $\alpha$] The proportion of agent-generated traffic in the session mixture.
\item[Non-stationary Noise $\epsilon_t$] Time-varying residual variation not explained by the actor mixture.
\item[Pricing Policy $\pi(\tau)$] A function mapping observed interaction history to an offered price.
\item[Cost of Information (COI)] The expected premium above the minimum viable price induced by the pricing policy.
\item[COI Leakage] A per-quote penalty term modeling information revealed to reconnaissance behavior.
\item[First-Order Statistic $p_{(1)}$] The minimum observed price among multiple independent queries.
\item[Transition Kernel $\mathcal{T}$] A Markov transition matrix over behavioral states or actions.
\item[Distinguishability] The degree to which human and agent sessions can be distinguished from behavior alone.
\item[KL Divergence $D_{KL}$] A relative-entropy measure used to compare session transition structure against class prototypes.
\item[Divergence Scores $\Delta_H,\Delta_A$] Session-level distances to human and agent transition centroids.
\item[Weak Agent Probability $f(\tau)$] A session-level score estimating the likelihood that a trajectory is agent-generated.
\item[Contamination Generator $\mathcal{G}(\alpha)$] A simulator component that injects synthetic agent trajectories to reach a target mixture level.
\item[Stackelberg Game] A leader-follower formulation where the platform sets prices and demand responds.
\item[Ambiguity Set $\mathcal{U}_{\epsilon}$] A set of plausible demand distributions considered under distributional uncertainty.
\item[Wasserstein Ball] A distance-bounded neighborhood around an empirical distribution used in robust optimization.
\item[DR-RL] Distributionally Robust Reinforcement Learning for policies trained against worst-case distributional shifts.
\item[Nominal Contamination $\alpha_0$] The baseline contamination level around which robust candidates are evaluated.
\item[Robustness Radius $\epsilon_\alpha$] The local interval width used for inner minimization over contamination scenarios.
\item[Query-Tax Surrogate] A constant leakage proxy assigning fixed penalty to suspected reconnaissance queries.
\item[Revelation Surrogate] A leakage proxy based on $-\log\pi(p\mid\tau)$ to penalize highly informative quotes.
\item[Limbo Stack] The alternating game-history buffer that stores leader price moves and follower demand responses.
\item[UX Index] A bounded user-experience metric tracked to evaluate policy side effects on legitimate users.
\item[Look-to-Book Ratio] The ratio of search-like interactions to completed purchases, used as an operational contamination indicator.
\item[Hybrid Kappa-Lambda Architecture] A data design combining streaming ingestion with offline and batch learning loops.
\item[MDP / POMDP] Sequential decision models with full observability (MDP) or partial observability (POMDP).
\item[Behavioral Model] A model predicting what action is likely to follow from prior actions.
\item[LLM] Large Language Model served through an inference provider with tool-use capability.
\item[TPU] Tensor Processing Unit, a specialized accelerator architecture developed by Google.
\end{description}

\section{Aggregate Compute Budget Derivation}
\label{app:compute_budget}

The claimed peak throughput of approximately 160\,PFLOPS follows from multiplying the per-chip BF16 peak (from official Google Cloud TPU documentation) by the number of chips in each allocation tier and summing across generations.

\begin{table}[ht]
\centering
\caption{Per-generation contribution to aggregate BF16 throughput.}
\label{tab:compute_derivation}
\begin{tabular}{@{}lrrr@{}}
\toprule
\textbf{TPU Gen.} & \textbf{Chips} & \textbf{Peak BF16/chip (TFLOPS)} & \textbf{Subtotal (TFLOPS)} \\
\midrule
v6e (Trillium) & 128 & 918 & $128 \times 918 = 117{,}504$ \\
v5e            & 128 & 197 & $128 \times 197 = 25{,}216$  \\
v4             &  64 & 275 & $64  \times 275 = 17{,}600$  \\
\midrule
\textbf{Total} & \textbf{320} & & $\mathbf{160{,}320}$ \\
\bottomrule
\end{tabular}
\end{table}

Converting to petaFLOPS: $160{,}320\;\text{TFLOPS} = 160.32\;\text{PFLOPS} \approx 160\;\text{PFLOPS}$. This is the theoretical peak under sustained BF16 arithmetic; realized throughput depends on memory bandwidth utilization and inter-chip communication overhead, but the figure serves as a useful upper bound for provisioning decisions.

\section{Slope-Test Verification: Revenue vs. Contamination}
\label{app:alpha_revenue_slope}

This appendix provides a compact verification of the slope result reported in the main results section. Using the same run-level pairs $x_i=\texttt{study/alpha}_i$ and $y_i=\texttt{eval/revenue\_mean}_i$ ($n=95$), we re-checked the ordinary least squares slope test in Python with standard test routines (SciPy two-sided $t$ test for the slope).

\[
\widehat{y}=326{,}878.57-60{,}631.95\,x,
\]
\[
t(93)=-8.2148,\qquad p=1.2038\times 10^{-12},\qquad R^2=0.4205,\qquad 95\%\,\text{CI}_{\beta_1}=[-75{,}288.76,\,-45{,}975.13].
\]

The Python verification reproduces the reported coefficients and inference values, confirming that the slope-test results are correct under standard methods.

\section{whoclickedit Dataset Card}
\label{app:whoclicked_card}

For transparency and reproducibility, this appendix includes the full dataset card used for the public release of the \texttt{whoclickedit} dataset.

\lstinputlisting[
  caption={whoclickedit dataset card (README snapshot)},
  label={lst:whoclicked_dataset_card}
]{chapters/auto/whoclicked_dataset_card.md}

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