Personalised versus Posted Pricing from Samples
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.
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BibTeX
@misc{kleer2026personalised,
title = {{Personalised versus Posted Pricing from Samples}},
author = {Pieter Kleer and Johan van Leeuwaarden and Daan Noordenbos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28181},
eprint = {2609.28181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28181},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Personalised versus Posted Pricing from Samples
AU - Pieter Kleer
AU - Johan van Leeuwaarden
AU - Daan Noordenbos
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28181
UR - https://arxiv.org/abs/2609.28181
AB - 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.
ER -