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fixing assumption definition

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Daniel Rosel
2026-02-14 21:54:42 +01:00
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paper/src/chapters/03-methodology.tex
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@@ -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. 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. 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] \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. 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.