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arXiv · 2108.00979

Generalized permutahedra and optimal auctions

Michael Joswig·Max Klimm·Sylvain Spitz
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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.

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Michael Joswig, Max Klimm, Sylvain Spitz. 2021-08-02. Generalized permutahedra and optimal auctions. https://arxiv.org/abs/2108.00979

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