{"ID":2892332,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15735","arxiv_id":"2507.15735","title":"The Root of Revenue Continuity","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.","short_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 thi...","url_abs":"https://arxiv.org/abs/2507.15735","url_pdf":"https://arxiv.org/pdf/2507.15735v2","authors":"[\"Sergiu Hart\",\"Noam Nisan\"]","published":"2025-07-21T15:42:41Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"econ.TH\"]","methods":"[]","has_code":false}