Generalized permutahedra and optimal auctions (Michael Joswig, Max Klimm and Sylvain Spitz)
SIAM Journal on Applied Algebra and Geometry, to appear.
@article{JoswigKlimmSpitz2022,
author = {Michael Joswig and Max Klimm and Sylvain Spitz},
title = {Generalized permutahedra and optimal auctions},
journal = {SIAM Journal on Applied Algebra and Geometry},
year = {to appear},
accepted = {30.09.2022},
}
We study a family of convex polytopes, called SIM-bodies, which were introduced by Giannakopoulos and Koutsoupias (2018) to analyze so-called Straight-Jacket Auctions. First, we show that the SIM-bodies belong to the class of generalized permutahedra. Second, we prove an optimality result for the Straight-Jacket Auctions among certain deterministic auctions. Third, we employ computer algebra methods and mathematical software to explicitly determine optimal prices and revenues.
