diff --git a/paper/src/chapters/03-methodology.tex b/paper/src/chapters/03-methodology.tex index fef7957..9258a80 100644 --- a/paper/src/chapters/03-methodology.tex +++ b/paper/src/chapters/03-methodology.tex @@ -92,9 +92,7 @@ where $\mathbb{E}[P]$ is the expected price charged by the policy and $\underlin We now formally demonstrate that standard dynamic pricing mechanisms are not incentive-compatible with high-frequency agentic traffic. As the number of independent competitive agents $N$ querying the system grows, the platform's ability to sustain a COI vanishes. -\begin{assumption} A fundamental assumption for our claim lays in the alignment of the AI agent through it's prompt which has been demonstrated by \cite{fish_algorithmic_2025} to cause strong collusive behavior under linguistic nudges. This assumption can be generalized to the human user asking the agent to research products with a minimizing objective. -\end{assumption} \begin{theorem}[COI Erosion in the Limit] Let $N$ be the number of independent, utility-maximizing agents querying the platform. Let $p_{(1)}$ be the first order statistic (minimum) of the prices offered to these agents. As $N \to \infty$, the Cost of Information converges to 0.