Georgia Institute of Technology College of Sciences

In finite games, a Nash equilibrium occurs when no player can increase their payoff by changing their strategy unless others do. According to J. Nash, such a game always has at least one Nash equilibrium when mixed strategies are allowed. This talk discusses when games have an unexpected number of totally mixed Nash equilibrium points. Such games form varieties called Nash discriminants. The main goal of this talk is to discuss a vector bundle approach to exploring the geometric properties of Nash discriminants. Part of this talk is based on joint work with Irem Portakal and Luca Sodomaco.