The Polyhedral Geometry of Truthful Auctions Article Swipe
Related Concepts
Common value auction
Unit cube
Set (abstract data type)
Outcome (game theory)
Unit (ring theory)
Mathematics
Construct (python library)
Cube (algebra)
Combinatorics
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Mathematical economics
Statistics
Programming language
Mathematics education
Michael Joswig
,
Max Klimm
,
Sylvain Spitz
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2211.01907
· OA: W4308244944
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2211.01907
· OA: W4308244944
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. This observation is then used to construct mechanisms that are robust in the sense that the set of items allocated to a player does change only slightly when the player's reported type is changed slightly.
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