The Simple Geometry of Perfect Information Games, International Journal of Game Theory
Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.
Jeroen Swinkels, Klaus Ritzberger, Stefano Demichelis
Swinkels, Jeroen, Klaus Ritzberger, and Stefano Demichelis. 2004. The Simple Geometry of Perfect Information Games. International Journal of Game Theory.(32): 315-338.