Academic Journal
Optimal Auction Design with Deferred Inspection and Reward.
| Title: | Optimal Auction Design with Deferred Inspection and Reward. |
|---|---|
| Authors: | Alaei, Saeed1 (AUTHOR) saeed.a@gmail.com, Belloni, Alexandre2,3 (AUTHOR) alexandre.belloni@duke.edu, Makhdoumi, Ali3 (AUTHOR) ali.makhdoumi@duke.edu, Malekian, Azarakhsh4 (AUTHOR) azarakhsh.malekian@rotman.utoronto.ca |
| Source: | Operations Research. Nov/Dec2024, Vol. 72 Issue 6, p2413-2429. 17p. |
| Subject Terms: | *Auctioneers, *Revenue management, *Data analytics, Calculus of variations, Continuous functions |
| Abstract: | In a variety of auction contexts, particularly those facilitated by digital marketplaces, auctioneers are now empowered to review the valuations submitted by purchasers and modify the final payments accordingly. Alaei et al. formulate and study the optimal design of such auctions, demonstrating that both the analysis and implementation vastly depart from classical settings. In particular, the analysis requires tools from convex analysis and the calculus of variations, which could be of independent interest in other mechanism design questions. Consider a mechanism run by an auctioneer who can use both payment and inspection instruments to incentivize agents. The timeline of the events is as follows. Based on a prespecified allocation rule and the reported values of agents, the auctioneer allocates the item and secures the reported values as deposits. The auctioneer then inspects the values of agents and, using a prespecified reward rule, rewards the ones who have reported truthfully. Using techniques from convex analysis and calculus of variations, for any distribution of values, we fully characterize the optimal mechanism for a single agent. Using Border's theorem and duality, we find conditions under which our characterization extends to multiple agents. Interestingly, the optimal allocation function, unlike the classic settings without inspection, is not a threshold strategy and instead is an increasing and continuous function of the types. We also present an implementation of our optimal auction and show that it achieves a higher revenue than auctions in classic settings without inspection. This is because the inspection enables the auctioneer to charge payments closer to the agents' true values without creating incentives for them to deviate to lower types. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2020.0651. [ABSTRACT FROM AUTHOR] |
| Copyright of Operations Research 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.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimal Auction Design with Deferred Inspection and Reward. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Alaei%2C+Saeed%22">Alaei, Saeed</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> saeed.a@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Belloni%2C+Alexandre%22">Belloni, Alexandre</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> alexandre.belloni@duke.edu</i><br /><searchLink fieldCode="AR" term="%22Makhdoumi%2C+Ali%22">Makhdoumi, Ali</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> ali.makhdoumi@duke.edu</i><br /><searchLink fieldCode="AR" term="%22Malekian%2C+Azarakhsh%22">Malekian, Azarakhsh</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> azarakhsh.malekian@rotman.utoronto.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Operations+Research%22">Operations Research</searchLink>. Nov/Dec2024, Vol. 72 Issue 6, p2413-2429. 17p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Auctioneers%22">Auctioneers</searchLink><br />*<searchLink fieldCode="DE" term="%22Revenue+management%22">Revenue management</searchLink><br />*<searchLink fieldCode="DE" term="%22Data+analytics%22">Data analytics</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+functions%22">Continuous functions</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In a variety of auction contexts, particularly those facilitated by digital marketplaces, auctioneers are now empowered to review the valuations submitted by purchasers and modify the final payments accordingly. Alaei et al. formulate and study the optimal design of such auctions, demonstrating that both the analysis and implementation vastly depart from classical settings. In particular, the analysis requires tools from convex analysis and the calculus of variations, which could be of independent interest in other mechanism design questions. Consider a mechanism run by an auctioneer who can use both payment and inspection instruments to incentivize agents. The timeline of the events is as follows. Based on a prespecified allocation rule and the reported values of agents, the auctioneer allocates the item and secures the reported values as deposits. The auctioneer then inspects the values of agents and, using a prespecified reward rule, rewards the ones who have reported truthfully. Using techniques from convex analysis and calculus of variations, for any distribution of values, we fully characterize the optimal mechanism for a single agent. Using Border's theorem and duality, we find conditions under which our characterization extends to multiple agents. Interestingly, the optimal allocation function, unlike the classic settings without inspection, is not a threshold strategy and instead is an increasing and continuous function of the types. We also present an implementation of our optimal auction and show that it achieves a higher revenue than auctions in classic settings without inspection. This is because the inspection enables the auctioneer to charge payments closer to the agents' true values without creating incentives for them to deviate to lower types. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2020.0651. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Operations Research 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/opre.2020.0651 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 2413 Subjects: – SubjectFull: Auctioneers Type: general – SubjectFull: Revenue management Type: general – SubjectFull: Data analytics Type: general – SubjectFull: Calculus of variations Type: general – SubjectFull: Continuous functions Type: general Titles: – TitleFull: Optimal Auction Design with Deferred Inspection and Reward. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Alaei, Saeed – PersonEntity: Name: NameFull: Belloni, Alexandre – PersonEntity: Name: NameFull: Makhdoumi, Ali – PersonEntity: Name: NameFull: Malekian, Azarakhsh IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov/Dec2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 0030364X Numbering: – Type: volume Value: 72 – Type: issue Value: 6 Titles: – TitleFull: Operations Research Type: main |
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