The Root of Revenue Continuity

Sergiu Hart; Noam Nisan

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arXiv · 2507.15735

The Root of Revenue Continuity

Sergiu Hart·Noam Nisan

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Abstract

In the setup of selling one or more goods, various papers have shown, in various forms and for various purposes, that a small change in the distribution of a buyer's valuations may cause only a small change in the possible revenue that can be extracted. We prove a simple, clean, convenient, and general statement to this effect: let $X$ and $Y$ be random valuations on $k$ additive goods, and let $W(X,Y)$ be the Wasserstein (or "earth mover's") distance between them; then $$\left\vert \sqrt{Rev(X)}-\sqrt{Rev(Y)}\right\vert \le \sqrt{W(X,Y)}.$$ This further implies that a simple explicit modification of any optimal mechanism for $X$, namely, "uniform discounting," is guaranteed to be almost optimal for any $Y$ that is close to $X$ in the Wasserstein distance.

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BibTeX RIS

Sergiu Hart, Noam Nisan. 2025-07-21. The Root of Revenue Continuity. https://arxiv.org/abs/2507.15735

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