My mathematical interests are Algorithmic Game Theory, Discrete and Computational Geometry, as well as Tropical Geometry.

**Preprints and work in progress:**

1. *Michael Joswig, Max Klimm, Sylvain Spitz*:
**Generalized Permutahedra and Optimal Auctions**,
arxiv:2108.00979 (2021)

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.

My M.Sc. project was on revenue maximizing auction mechanisms, I have studied on the duality and optimality of a broad class of valuation densities in the 2-item setting. You can access the german version here.

*Last Update: March 9, 2021*