Abstract for the talk on 25.10.2021 (14:00 h)Numerical Algebra and Optimization Seminar
Sylvain Spitz (TU Berlin)
Generalized Permutahedra and Optimal Auctions
25.10.2021, 14:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)
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.