Generalized Permutahedra and Optimal Auctions

Explore a 34-minute lecture by Michael Joswig from the Hausdorff Center for Mathematics on generalized permutahedra and optimal auctions. Delve into the study of SIM-bodies, a family of convex polytopes introduced by Giannakopoulos and Koutsoupias in 2018 for analyzing Straight-Jacket Auctions. Discover how these SIM-bodies belong to the class of generalized permutahedra and learn about the optimality of Straight-Jacket Auctions among certain deterministic auctions. Gain insights into the use of computer algebra methods and mathematical software for determining optimal prices and revenues. Understand the connection between SIM-bodies and regions of linearity in tropical polynomials. This lecture presents joint work with Max Klimm and Sylvain Spitz, offering a comprehensive look at the intersection of geometry, optimization, and auction theory.