Generalized permutahedra and optimal auctions

TL;DR

This paper explores SIM-bodies, showing they are generalized permutahedra, and demonstrates the optimality of Straight-Jacket Auctions within a class of deterministic auctions, using computational methods to find optimal prices.

Contribution

It establishes the geometric nature of SIM-bodies as generalized permutahedra and proves the optimality of Straight-Jacket Auctions among certain deterministic auctions.

Findings

SIM-bodies are generalized permutahedra

Straight-Jacket Auctions are optimal among certain deterministic auctions

Explicit optimal prices and revenues are computed using software

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.