fixing mdp defintino

paper/src/chapters/03-methodology.tex

@@ -341,11 +341,11 @@ With these divergence features we compute a weak agent probability $f(\tau')\in[
 \label{sec:tpe}
 
 
-For both subsets, we model session dynamics as an MDP and estimate transition kernel $\mathcal{T}$. For each actor type we estimate global kernels $\hat{\mathcal{T}}_A$ and $\hat{\mathcal{T}}_H$, then cluster into behavioral sub-kernels $\hat{\mathcal{T}}_y^i$ to avoid collapsing all behavior into one average profile. Transition probabilities are estimated by maximum likelihood:
+For both subsets, we model session dynamics as a Markov decision process and estimate transition kernel $\mathcal{T}$. For each actor type we estimate global kernels $\hat{\mathcal{T}}_A$ and $\hat{\mathcal{T}}_H$, then cluster into behavioral sub-kernels $\hat{\mathcal{T}}_y^i$ to avoid collapsing all behavior into one average profile. Transition probabilities are estimated by maximum likelihood:
 \begin{equation}
     \hat{P}(s' \mid s) = \frac{N(s, s')}{\sum_{k \in \mathcal{S}} N(s, k)}
 \end{equation}
-where $N(s, s')$ is the observed transition count. This allows us to construct a \textit{Contamination Generator} $\mathcal{G}(\alpha)$. Given a clean trajectory dataset, $\mathcal{G}$ injects synthetic agent trajectories sampled from $\hat{\mathcal{T}}_A$ until the effective mixing ratio reaches $\alpha$. The properties of an MDP such as ... should be preserved by the operation described below.
+where $N(s, s')$ is the observed transition count. This allows us to construct a \textit{Contamination Generator} $\mathcal{G}(\alpha)$. Given a clean trajectory dataset, $\mathcal{G}$ injects synthetic agent trajectories sampled from $\hat{\mathcal{T}}_A$ until the effective mixing ratio reaches $\alpha$. The properties of an MDP such as a discrete state space, nonnegative transition mass, and row-stochasticity ($\sum_{s'}\hat{P}(s'\mid s)=1$ for visited states) should be preserved by the operation described below.
 
 To scale this to catalog-level pricing, we expand the base event transition matrix from $T\times T$ into product-specific transitions using the current demand condition. In practice, we normalize the demand vector across products and use it to weight how much transition mass each product pair receives. Concretely, each cell of the base matrix becomes an $N\times N$ block (for $N$ products), so the transition matrix grows from $T\times T$ to $(T\cdot N)\times(T\cdot N)$. Finally, we add $C$ generic states (homepage, login, checkout terminal states), which gives the full kernel size $(T\cdot N + C)\times(T\cdot N + C)$.
 % The validity of this demand-weighted block expansion is still subject to formal proof: it needs to be shown that the resulting matrix retains row-stochasticity (rows summing to 1) and that the weighting by the demand vector preserves the Markov property for the expanded state space. In the engine source this is the target of ongoing validation before the expansion is relied on for behavioral generation at scale.

paper/src/summary.tex

@@ -21,8 +21,8 @@
 
 \vspace{0.75em}
 
-To better understand all wedges of the current works, we must start by exploring the nature of agents, agentic computer use and web automation, complementing that with economic reasoning and strategic interaction.
-The final surface to cover leads us to data-driven dynamic pricing under uncertainty.
+Large language model (LLM) agents are spreading in e-commerce; one consequence is intermediaries that can separate information gathering from transaction execution.
+This thesis studies dynamic pricing when agents reconnoitre in isolated sessions and thereby weaken the \emph{Cost of Information} (COI), the premium platforms typically extract once demand signals are expressed.
 The key technical risk is not ``agents buying things'' per se, but agents shaping the behavioral and demand signals that downstream pricing systems consume and depend on \parencite{xia_evaluation-driven_2025}.
 Dynamic pricing assumes demand proxies are behaviorally meaningful, while bot detection aims at security and access control.
 The missing bridge is a principled framework for distinguishing non-human reconnaissance from genuine human demand expression and integrating that distinguishability into pricing heuristics without degrading legitimate user experience (in our research tracked by the user-experience index).