DUALITY AND OPTIMALITY OF AUCTIONS FOR UNIFORM DISTRIBUTIONS.
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| Title: | DUALITY AND OPTIMALITY OF AUCTIONS FOR UNIFORM DISTRIBUTIONS. |
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| Authors: | GIANNAKOPOULO, YIANNIS1 ygiannak@cs.ox.ac.uk, KOUTSOUPIAS, ELIAS1 elias@cs.ox.ac.uk |
| Source: | SIAM Journal on Computing. 2018, Vol. 47 Issue 1, p121-165. 45p. |
| Subjects: | Duality (Logic), Uniform distribution (Probability theory), Bayesian analysis |
| Abstract: | We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called straight-jacket auction (SJA), which we prove to be exactly optimal for up to six items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics 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: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 128574978 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: DUALITY AND OPTIMALITY OF AUCTIONS FOR UNIFORM DISTRIBUTIONS. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22GIANNAKOPOULO%2C+YIANNIS%22">GIANNAKOPOULO, YIANNIS</searchLink><relatesTo>1</relatesTo><i> ygiannak@cs.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22KOUTSOUPIAS%2C+ELIAS%22">KOUTSOUPIAS, ELIAS</searchLink><relatesTo>1</relatesTo><i> elias@cs.ox.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Computing%22">SIAM Journal on Computing</searchLink>. 2018, Vol. 47 Issue 1, p121-165. 45p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Duality+%28Logic%29%22">Duality (Logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Uniform+distribution+%28Probability+theory%29%22">Uniform distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+analysis%22">Bayesian analysis</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the geometric nature of the problem and highlights its connection with the theory of bipartite graph matchings. We demonstrate the power of the framework by applying it to a multiple-good monopoly setting where the buyer has uniformly distributed valuations for the items, the canonical long-standing open problem in the area. We propose a deterministic selling mechanism called straight-jacket auction (SJA), which we prove to be exactly optimal for up to six items, and conjecture its optimality for any number of goods. The duality framework is used not only for proving optimality, but perhaps more importantly for deriving the optimal mechanism itself; as a result, SJA is defined by natural geometric constraints. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics 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: 10.1137/16M1072218 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 45 StartPage: 121 Subjects: – SubjectFull: Duality (Logic) Type: general – SubjectFull: Uniform distribution (Probability theory) Type: general – SubjectFull: Bayesian analysis Type: general Titles: – TitleFull: DUALITY AND OPTIMALITY OF AUCTIONS FOR UNIFORM DISTRIBUTIONS. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: GIANNAKOPOULO, YIANNIS – PersonEntity: Name: NameFull: KOUTSOUPIAS, ELIAS IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 00975397 Numbering: – Type: volume Value: 47 – Type: issue Value: 1 Titles: – TitleFull: SIAM Journal on Computing Type: main |
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