{
  "abstract": "Personalised pricing maximises expected revenue from a market but requires detailed information about individual customers. How much of this revenue can be recovered using a simple posted price based on a finite number of samples from the underlying value distribution? We answer this question by maximising the worst-case ratio between the expected revenues of posted and personalised pricing over the fundamental class of $λ$-regular value distributions. Our results reveal a structural transition as a function of $λ$. For the class of monotone hazard rate (MHR) distributions, corresponding to $λ= 0$, the sample mean is an optimal statistic: the entire sample can be compressed into its average without any loss of revenue. Beyond the MHR class, corresponding to $λ> 0$, this property disappears. We show that the sample mean is no longer optimal, revealing that optimal sample-based pricing rules become substantially more intricate. Nevertheless, we show that a remarkably simple order-statistic based pricing rule is asymptotically optimal as the number of samples $n$ grows, achieving the optimal approximation ratio up to a tight error of order $1/n$. Our analysis combines techniques from probability, approximation theory and optimization, including doubly infinite linear programming, hypergeometric functions, and combinatorial identities involving incomplete Beta functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28181",
  "author_total": 3,
  "authors": [
    {
      "name": "Pieter Kleer"
    },
    {
      "name": "Johan van Leeuwaarden"
    },
    {
      "name": "Daan Noordenbos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8ytvkpe53t88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28181",
  "fulltext_url": null,
  "id": "b8ytvkpe53t88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28181",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Auction Theory and Applications"
    ]
  ],
  "openalex": "W7214243365",
  "pdf_url": "https://arxiv.org/pdf/2609.28181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8ytvkpe53t88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Personalised versus Posted Pricing from Samples",
  "title_text": "Personalised versus Posted Pricing from Samples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/b8ytvkpe53t88",
  "venue": "arXiv",
  "versions": []
}