| Speaker: | Hirotachi Abo (University of idaho) |
|---|---|
| Title: | An algebro-geometric approach to Nash equilibria |
| Date (JST): | Thu, Jun 12, 2025, 15:30 - 17:00 |
| Place: | Seminar Room B |
| Abstract: |
Mixed Nash equilibrium is a concept in game theory that determines an optimal solution of a non-cooperative finite game. Using so-called payoff tensors (tensors that express the possible choices for the players and the outcomes of such decisions), one can interpret mixed Nash equilibria as points in the tensor space (called Nash equilibrium points). In this talk, we discuss an algebro-geometric interpretation of the expected number of "totally" mixed Nash equilibrium points for a “generic” game (the game with generic payoff tensors) obtained by R. McKelvey and A. McLennan. The payoff tensors with which the game has an unexpected number of Nash equilibrium points form a variety. I will also talk about the geometry of such a variety. This is joint work with Irem Portakal and Luca Sodomaco. |
