Academic Journal
The I.I.D. Prophet Inequality with Limited Flexibility.
| Title: | The I.I.D. Prophet Inequality with Limited Flexibility. |
|---|---|
| Authors: | Perez-Salazar, Sebastian1 (AUTHOR) sperez@rice.edu, Singh, Mohit2 (AUTHOR) mohit.singh@isye.gatech.edu, Toriello, Alejandro2 (AUTHOR) atoriello@isye.gatech.edu |
| Source: | Mathematics of Operations Research (INFORMS). Feb2026, Vol. 51 Issue 1, p218-254. 37p. |
| Subject Terms: | *Time-based pricing, *Linear programming, *Internet sales, Approximation algorithms |
| Abstract: | In online sales, sellers usually offer each potential buyer a posted price in a take-it-or-leave fashion. Buyers can sometimes see posted prices faced by other buyers, and changing the price frequently could be considered unfair. The literature on posted-price mechanisms and prophet inequality problems has studied the two extremes of pricing policies, the fixed-price policy and fully dynamic pricing. The former is suboptimal in revenue but is perceived as fairer than the latter. This work examines the middle situation, where there are at most k distinct prices over the selling horizon. Using the framework of prophet inequalities with independent and identically distributed random variables, we propose a new prophet inequality for strategies that use at most k thresholds. We present asymptotic results in k and results for small values of k. For k = 2 prices, we show an improvement of at least 11% over the best fixed-price solution. Moreover, k = 5 prices suffice to guarantee almost 99% of the approximation factor obtained by a fully dynamic policy that uses an arbitrary number of prices. From a technical standpoint, we use an infinite-dimensional linear program in our analysis; this formulation could be of independent interest to other online selection problems. Funding: This research was supported by the U.S. National Science Foundation [Grants CCF-2106444, CCF-1910423, and CMMI 1552479]. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Business Source Index |
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| Items | – Name: Title Label: Title Group: Ti Data: The I.I.D. Prophet Inequality with Limited Flexibility. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Perez-Salazar%2C+Sebastian%22">Perez-Salazar, Sebastian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sperez@rice.edu</i><br /><searchLink fieldCode="AR" term="%22Singh%2C+Mohit%22">Singh, Mohit</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> mohit.singh@isye.gatech.edu</i><br /><searchLink fieldCode="AR" term="%22Toriello%2C+Alejandro%22">Toriello, Alejandro</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> atoriello@isye.gatech.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematics+of+Operations+Research+%28INFORMS%29%22">Mathematics of Operations Research (INFORMS)</searchLink>. Feb2026, Vol. 51 Issue 1, p218-254. 37p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Time-based+pricing%22">Time-based pricing</searchLink><br />*<searchLink fieldCode="DE" term="%22Linear+programming%22">Linear programming</searchLink><br />*<searchLink fieldCode="DE" term="%22Internet+sales%22">Internet sales</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+algorithms%22">Approximation algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In online sales, sellers usually offer each potential buyer a posted price in a take-it-or-leave fashion. Buyers can sometimes see posted prices faced by other buyers, and changing the price frequently could be considered unfair. The literature on posted-price mechanisms and prophet inequality problems has studied the two extremes of pricing policies, the fixed-price policy and fully dynamic pricing. The former is suboptimal in revenue but is perceived as fairer than the latter. This work examines the middle situation, where there are at most k distinct prices over the selling horizon. Using the framework of prophet inequalities with independent and identically distributed random variables, we propose a new prophet inequality for strategies that use at most k thresholds. We present asymptotic results in k and results for small values of k. For k = 2 prices, we show an improvement of at least 11% over the best fixed-price solution. Moreover, k = 5 prices suffice to guarantee almost 99% of the approximation factor obtained by a fully dynamic policy that uses an arbitrary number of prices. From a technical standpoint, we use an infinite-dimensional linear program in our analysis; this formulation could be of independent interest to other online selection problems. Funding: This research was supported by the U.S. National Science Foundation [Grants CCF-2106444, CCF-1910423, and CMMI 1552479]. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematics of Operations Research (INFORMS) is the property of INFORMS: Institute for Operations Research & the Management Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1287/moor.2022.0345 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 37 StartPage: 218 Subjects: – SubjectFull: Time-based pricing Type: general – SubjectFull: Linear programming Type: general – SubjectFull: Internet sales Type: general – SubjectFull: Approximation algorithms Type: general Titles: – TitleFull: The I.I.D. Prophet Inequality with Limited Flexibility. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Perez-Salazar, Sebastian – PersonEntity: Name: NameFull: Singh, Mohit – PersonEntity: Name: NameFull: Toriello, Alejandro IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0364765X Numbering: – Type: volume Value: 51 – Type: issue Value: 1 Titles: – TitleFull: Mathematics of Operations Research (INFORMS) Type: main |
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