The M9 Research Seminar is a weekly seminar in which our guests as well as our group discuss recent research advances and interesting open problems in applied geometry and discrete mathematics.

Usual time: Monday 15:15

Usual room: 02.04.011

Past and Upcoming Talks

Date	Speaker	Title
Jul 17, 2017, 13:00	Florian Speicher	Vorstellung für AdONE
Jul 07, 2017, 10:00	Bernhard von Stengel (London School of Economics)	Index and Uniqueness of Symmetric Equilibria @MI 02.06.011

Abstracts

Florian Speicher: Vorstellung für AdONE

Im Rahmen des AdONE-Graduiertenkollegs (http://www.gs.tum.de/adone/start/) stellt sich Herr Florian Speicher vor und berichtet über sein aktuelles Forschungsprojekt bei BMW. Interessierte sind herzlich eingeladen.

Bernhard von Stengel (London School of Economics): Index and Uniqueness of Symmetric Equilibria @MI 02.06.011

In a symmetric two-player game, a symmetric equilibrium can only be dynamically stable if it has positive index. The sum of the indices of all equilibria is 1, so a unique equilibrium has index 1. The index is a topological notion related to geometric orientation, and defined in terms of the sign of the determinant of the payoffs in the equilibrium support. We prove a simple strategic characterization of the index conjectured by Hofbauer: In a nondegenerate symmetric game, an equilibrium has index 1 if and only if it is the unique equilibrium in a larger symmetric game obtained by adding further strategies (it suffices to add a linear number of strategies).

Our elementary proof introduces "unit-vector games" where one player's payoff matrix consists of unit vectors, and applies in a novel way simplicial polytopes. In addition, we employ a very different known result that any matrix with positive determinant is the product of three P-matrices, a class of matrices important in linear complementarity.

Joint work with Anne Balthasar.

Talk will take place in MI 02.06.011