Javier Sendra Arranz: Algebraic Geometry meets Game Theory: Spohn CI varieties

Abstract

The goal of algebraic game theory is to employ algebro-geometric tools to analyse distinct notions of equilibria of games. These synergies between algebraic geometry and game theory have been beneficial in the study of Nash and dependency equilibria. These two notions models the situation where where the players behave independently and collectively respectively. In between these opposite cases, many dependencies among the players may occur. The conditional independence (CI) equilibria of an undirected graph deals with the scenario where the dependencies of the players are modelled by a graph whose vertices represent the players. In this talk we focus on binary games and we analyse the CI equilibria of an undirected graph from the algebro-geometric study of the Spohn CI variety. This is based on a join work with Irem Portakal.