The polyhedral geometry of truthful auctions: The polyhedral geometry of truthful...: M. Joswig et al.
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| Title: | The polyhedral geometry of truthful auctions: The polyhedral geometry of truthful...: M. Joswig et al. |
|---|---|
| Authors: | Joswig, Michael1,2 (AUTHOR) joswig@math.tu-berlin.de, Klimm, Max3 (AUTHOR) klimm@math.tu-berlin.de, Spitz, Sylvain3 (AUTHOR) spitz@math.tu-berlin.de |
| Source: | Mathematical Programming. Mar2025, Vol. 210 Issue 1, p539-566. 28p. |
| Subjects: | Affine geometry, Difference sets, Incentive (Psychology), Auctions, Geometry |
| Abstract: | The difference set of an outcome in an auction is the set of types that the auction mechanism maps to the outcome. We give a complete characterization of the geometry of the difference sets that can appear for a dominant strategy incentive compatible multi-unit auction showing that they correspond to regular subdivisions of the unit cube. Similarly, we describe the geometry for affine maximizers for n players and m items, showing that they correspond to regular subdivisions of the m-fold product of (n - 1) -dimensional simplices. These observations are then used to construct mechanisms that are robust in the sense that the sets of items allocated to the players change only slightly when the players' reported types are changed slightly. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Programming is the property of Springer Nature 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 183375673 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The polyhedral geometry of truthful auctions: The polyhedral geometry of truthful...: M. Joswig et al. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Joswig%2C+Michael%22">Joswig, Michael</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> joswig@math.tu-berlin.de</i><br /><searchLink fieldCode="AR" term="%22Klimm%2C+Max%22">Klimm, Max</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> klimm@math.tu-berlin.de</i><br /><searchLink fieldCode="AR" term="%22Spitz%2C+Sylvain%22">Spitz, Sylvain</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> spitz@math.tu-berlin.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Programming%22">Mathematical Programming</searchLink>. Mar2025, Vol. 210 Issue 1, p539-566. 28p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Affine+geometry%22">Affine geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Difference+sets%22">Difference sets</searchLink><br /><searchLink fieldCode="DE" term="%22Incentive+%28Psychology%29%22">Incentive (Psychology)</searchLink><br /><searchLink fieldCode="DE" term="%22Auctions%22">Auctions</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The difference set of an outcome in an auction is the set of types that the auction mechanism maps to the outcome. We give a complete characterization of the geometry of the difference sets that can appear for a dominant strategy incentive compatible multi-unit auction showing that they correspond to regular subdivisions of the unit cube. Similarly, we describe the geometry for affine maximizers for n players and m items, showing that they correspond to regular subdivisions of the m-fold product of (n - 1) -dimensional simplices. These observations are then used to construct mechanisms that are robust in the sense that the sets of items allocated to the players change only slightly when the players' reported types are changed slightly. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Programming is the property of Springer Nature 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: 10.1007/s10107-024-02168-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 539 Subjects: – SubjectFull: Affine geometry Type: general – SubjectFull: Difference sets Type: general – SubjectFull: Incentive (Psychology) Type: general – SubjectFull: Auctions Type: general – SubjectFull: Geometry Type: general Titles: – TitleFull: The polyhedral geometry of truthful auctions: The polyhedral geometry of truthful...: M. Joswig et al. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Joswig, Michael – PersonEntity: Name: NameFull: Klimm, Max – PersonEntity: Name: NameFull: Spitz, Sylvain IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00255610 Numbering: – Type: volume Value: 210 – Type: issue Value: 1 Titles: – TitleFull: Mathematical Programming Type: main |
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