Sylvain Spitz

 

Fakultät II - Mathematik und Naturwissenschaften
Institut für Mathematik
Technische Universität Berlin
Straße des 17. Juni 136
10623 Berlin

Office: MA 514
Telephone: +49 30 314 78657
Email: (lastname)@math.tu-berlin.de

Projects

• Combinatorial Network Flow Methods for Instationary Gas Flows and Gas Market Problems (Phase 3)
  SFB Transregio TRR154 Deutsche Forschungsgemeinschaft (DFG). Project heads: Max Klimm, Marc Pfetsch and Martin Skutella
• Tropical Mechanism Design
  Math+ project AA3-5. Project heads: Michael Joswig and Max Klimm

Publications

to appear

• The Polyhedral Geometry of Truthful Auctions (Michael Joswig, Max Klimm and Sylvain Spitz)
  IPCO 2023 – Proc. 24th Conference on Integer Programming and Combinatorial Optimization.
  Bibtex Abstract
  @inproceedings{JoswigKlimmSpitz2023,
  author = {Michael Joswig and Max Klimm and Sylvain Spitz},
  title = {The Polyhedral Geometry of Truthful Auctions},
  booktitle = {IPCO 2023 – Proc. 24th Conference on Integer Programming and Combinatorial Optimization},
  year = {to appear},
  accepted = {20.01.2023},
  }
  
  The difference set of an outcome in an auction is the set of types that the auction mechanism maps to the outcome. We give a complete characterization of the geometry of the difference sets that can appear for a dominant strategy incentive compatible multi-unit auction showing that they correspond to regular subdivisions of the unit cube. This observation is then used to construct mechanisms that are robust in the sense that the set of items allocated to a player does change only slightly when the player's reported type is changed slightly.

2022

• Generalized Permutahedra and Optimal Auctions (Michael Joswig, Max Klimm and Sylvain Spitz)
  SIAM Journal on Applied Algebra and Geometry, 6(1):711-739, 2022.
  DOI Bibtex Abstract
  @article{JoswigKlimmSpitz2022,
  author = {Michael Joswig and Max Klimm and Sylvain Spitz},
  title = {Generalized Permutahedra and Optimal Auctions},
  journal = {SIAM Journal on Applied Algebra and Geometry},
  year = {2022},
  volume = {6},
  number = {1},
  pages = {711-739},
  accepted = {30.09.2022},
  doi = {10.1137/21M1441286},
  }
  
  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.