Game theory is an area that has historically benefited greatly from outside ideas. In 1950, Nash published a very influential two-page paper proving the existence of Nash equilibria for any finite game. The proof uses an elegant application of the Kakutani fixed-point theorem from the field of topology. This opened a new horizon not only in game theory, but also in areas such as economics, computer science, evolutionary biology, and social sciences. In this talk, we model different notions of equilibria in terms of undirected graphical models.The vertices of the underlying graph of the graphical model represent the players of the game and the dependencies of the choices of the players are depicted with an edge in the graph. This approach brings game theory in contact with the field of algebraic statistics for the first time, which offers a strong foundation for utilizing algebro-geometric tools to solve interesting problems in game theory. This is joint work with Javier Sendra-Arranz and Bernd Sturmfels.