Generalized permutahedra and optimal auctions
Metric Geometry
2021-08-03 v1 Computer Science and Game Theory
Optimization and Control
Abstract
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.
Cite
@article{arxiv.2108.00979,
title = {Generalized permutahedra and optimal auctions},
author = {Michael Joswig and Max Klimm and Sylvain Spitz},
journal= {arXiv preprint arXiv:2108.00979},
year = {2021}
}
Comments
24 pages, 2 figures