Goethe-Universität — Irem Portakal: Algebraic methods for Nash equilibrium

Frankfurter Seminar - Kolloquium des Instituts für Mathematik

Ginkgo Seminar

Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende

An den jeweiligen Veranstaltungstagen wird mit dem Ginkgo-Seminar (Gingko - Grundlagen, Intuition, Neugier für und auf das Kolloquium) gestartet, einer exklusiven Veranstaltung von Doktoranden für Doktoranden, Post-Docs und interessierte Studierende.

Ziel ist es, die Vorträge "aus der anderen Ecke des Instituts" für alle Interessierten zugänglicher zu machen.

Das Vorkolloquium findet immer ab 15.00 (c.t.) in Raum 711 groß vor dem jeweiligen Vortrag statt.

Frankfurter Seminar

Jan 28 2026

16:45

Irem Portakal: Algebraic methods for Nash equilibrium

MPI Leipzig

Abstract: The set of Nash equilibria of a finite game admits a natural description as a semi-algebraic set, that is, defined by a finite system of polynomial equalities and inequalities whose variables correspond to the mixed strategies of the players. This algebraic viewpoint oﬀers both conceptual and computational insights into the study of equilibrium.

The talk will begin with a brief introduction to the basic setup of finite games and the definiton of Nash equilibrium, emphasizing the underlying polynomial structure.

We will then discuss how this description enables the application of tools from real algebraic geometry to game theory. In particular, we will highlight classical and recent results concerning the maximal number of Nash equilibria in generic games and explore how these bounds reflect the geometry of the corresponding solution sets.