Tensors, Nash, and Other Equilibria
- Irem Portakal (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)
In this ongoing joint project with Bernd Sturmfels, we explore the polynomial systems arising from Nash, correlated and dependency equilibria in Game Theory. Nash equilibria are given by a real algebraic variety in the tensor space of probability distributions of rank 1. In this case one assumes the causal independence of the actions and decisions of the players. If one drops this assumption i.e. the rank 1 condition, one encounters the correlated (Aumann, 1974) and dependency (Spohn, 2003) equilibria. For any finite game, those three equilibria always exist by the famous result of Nash in 1951. In this talk, we follow these concepts on 2-person games in which each player has two strategies and present a glance for the general case.