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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 00255610 |
| DOI: | 10.1007/s10107-024-02168-y |
